From fae81cb7551ac447b299d231439f9cea886cc813 Mon Sep 17 00:00:00 2001
From: CalMacCQ <93673602+CalMacCQ@users.noreply.github.com>
Date: Thu, 19 Dec 2024 15:02:44 +0000
Subject: [PATCH 01/17] add QAOA notebook

---
 .../pytket_qaoa_maxcut_example.ipynb          | 768 ++++++++++++++++++
 1 file changed, 768 insertions(+)
 create mode 100644 docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb

diff --git a/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb b/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb
new file mode 100644
index 00000000..924ae35d
--- /dev/null
+++ b/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb
@@ -0,0 +1,768 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "a3ba3449",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "slide"
+    }
+   },
+   "source": [
+    "# The Quantum Approximate Optimisation Algorithm (QAOA) using TKET."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "45668632",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "subslide"
+    }
+   },
+   "source": [
+    "## The Max-Cut problem"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "9456fbeb",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "fragment"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "import networkx as nx\n",
+    "import matplotlib.pyplot as plt\n",
+    "G = nx.Graph()\n",
+    "G.add_edges_from([(0, 1), (1, 2), (2, 0)])\n",
+    "plt.figure(figsize=(2, 2))\n",
+    "nx.draw(G, node_color=['red', 'blue', 'red'])\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "cad41481",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "fragment"
+    }
+   },
+   "source": [
+    "There are $2^3$ possible assignments of colour to nodes. In general there are $2^n$. The Max-cut problem can then be stated as that of finding the colour assignment which maximises the number of edges between vertices of a different colour."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7389bbe5",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "subslide"
+    }
+   },
+   "source": [
+    "## Quantum Approximate Optimization Algorithm (QAOA)\n",
+    "\n",
+    "Introduced in 'A Quantum Approximate Optimization Algorithm' (found at https://arxiv.org/abs/1411.4028). The idea is to prepare a quantum state which encodes a solution to the Max-cut problem.\n",
+    "\n",
+    "\n",
+    "This is a variational algorithm, which is to say that a paramaterised state is prepared, with the parameters varied to improve the solution. We will have $2p$ parameters where p is our number of layers. In particular, the state prepared has the form \n",
+    "\n",
+    "\n",
+    "$$\n",
+    "| \\psi  ( \\beta, \\gamma ) \\rangle = U ( \\beta_m ) U ( \\gamma_m ) ... U (\\beta_0) U ( \\gamma_0 ) | \\psi_0 \\rangle\n",
+    "$$\n",
+    "where\n",
+    "$$\n",
+    "U( \\beta_i ) = e^{i \\beta H_B} \\quad \\& \\quad U ( \\gamma_i) = e^{i \\gamma H_P}\n",
+    "$$\n",
+    "with $H_P$ depending on the problem instance. "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3596e66d",
+   "metadata": {},
+   "source": [
+    "## Cost function for Maxcut\n",
+    "$$\n",
+    "\\begin{equation}\n",
+    "C= \\sum_{(i,\\,j)} x_i(1-x_j)\n",
+    "\\end{equation}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d720b387",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "subslide"
+    }
+   },
+   "source": [
+    "For the previous 3 vertex graph the *problem Hamiltonian* is\n",
+    "$$\n",
+    "H_P = \\frac{1}{2} \\Big[ ( Z \\otimes Z \\otimes I ) + ( Z \\otimes I \\otimes Z ) + ( I \\otimes Z \\otimes Z ) \\Big]\n",
+    "$$\n",
+    "\n",
+    "where you will notice that there is a $ Z \\otimes Z$ acting between each vertex which is connected by an edge."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8ca2e1b9",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "fragment"
+    }
+   },
+   "source": [
+    "The *mixer Hamiltonian* has the form \n",
+    "$$\n",
+    "H_B =   ( X \\otimes I \\otimes I ) + ( I \\otimes X \\otimes I ) + ( I \\otimes I \\otimes X )\n",
+    "$$\n",
+    "\n",
+    "where you will notice that there is an $X$ operator acting on each vertex."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "de6b9e03",
+   "metadata": {},
+   "source": [
+    "## Cost function for Maxcut\n",
+    "\n",
+    "A solution to maxcut can be found by maximising the following cost function $C$ .\n",
+    "\n",
+    "\n",
+    "\n",
+    "$$\n",
+    "\\begin{equation}\n",
+    "C= \\sum_{(i,j)} x_i(1-x_j)\n",
+    "\\end{equation}\n",
+    "$$\n",
+    "\n",
+    "Here $x_i$ and $x_j$ are the the \"colours\" of each vertex.  \n",
+    "\n",
+    "$$\n",
+    "\\begin{equation}\n",
+    "x_i,x_j \\in \\{0,1\\}\n",
+    "\\end{equation}\n",
+    "$$\n",
+    "\n",
+    "$x_i(1-x_j)=0$ if $x_i=x_j$ and $ x_i(1-x_j)=1$ if the terms are not equal."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "61d4e798",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "slide"
+    }
+   },
+   "source": [
+    "We want to encode our Maxcut cost function as a Hamiltonain. To do this we can perform the following translation.\n",
+    "\n",
+    "$$\n",
+    "\\begin{equation}\n",
+    "x_i \\mapsto \\frac{1}{2}(I-Z_i)\n",
+    "\\end{equation}\n",
+    "$$\n",
+    "\n",
+    "\n",
+    "The Pauli Z operator can be used to distinguish between the $|0\\rangle$ and $|1\\rangle$ basis states as these are eigenstates with eigenvalues $\\pm 1$ .\n",
+    "\n",
+    "$$\n",
+    "\\begin{equation}\n",
+    "H_P = \\frac{1}{2}\\sum_{(i, \\,j)} (I-Z_i \\,Z_j)\n",
+    "\\end{equation}\n",
+    "$$\n",
+    "\n",
+    "\n",
+    "$$\n",
+    "\\begin{equation}\n",
+    "H_B = \\sum_i X_i\n",
+    "\\end{equation}\n",
+    "$$\n",
+    "\n",
+    "Here we use the the convention that $X_i$ means a Pauli X operator will be applied to the \"ith\" qubit and the identity operator will be applied to all other qubits in the circuit."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "aeb6abd9",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "skip"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "import warnings\n",
+    "warnings.filterwarnings(\"ignore\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3cbb783a",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "slide"
+    }
+   },
+   "source": [
+    "# Circuit Construction for QAOA"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "688f1332",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "slide"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "import networkx as nx\n",
+    "\n",
+    "max_cut_graph_edges = [(0,1), (1,2), (1,3), (3,4), (4,5), (4,6)]\n",
+    "n_nodes = 7\n",
+    "\n",
+    "max_cut_graph = nx.Graph()\n",
+    "max_cut_graph.add_edges_from(max_cut_graph_edges)\n",
+    "nx.draw(max_cut_graph, labels={node: node for node in max_cut_graph.nodes()})\n",
+    "\n",
+    "expected_results = [(0,1,0,0,1,0,0), (1,0,1,1,0,1,1)]"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "18a5bd16",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "slide"
+    }
+   },
+   "source": [
+    "## Define Cost Hamiltonian: $\\gamma H$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "543f87ca",
+   "metadata": {},
+   "source": [
+    "$$\n",
+    "\\begin{equation}\n",
+    "H_P = \\frac{1}{2}\\sum_{<jk>} (-Z_j \\,Z_k +I )\n",
+    "\\end{equation}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "99226b24",
+   "metadata": {
+    "scrolled": true,
+    "slideshow": {
+     "slide_type": "fragment"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "from typing import List, Tuple, Any\n",
+    "from pytket.utils import QubitPauliOperator\n",
+    "from pytket.pauli import QubitPauliString, Pauli\n",
+    "from pytket import Qubit\n",
+    "\n",
+    "def qaoa_graph_to_cost_hamiltonian(edges: List[Tuple[int, int]], cost_angle: float) -> QubitPauliOperator:\n",
+    "    qpo_dict = {QubitPauliString(): len(edges)*0.5*cost_angle}\n",
+    "    for e in edges:\n",
+    "        term_string = QubitPauliString([Qubit(e[0]), Qubit(e[1])], [Pauli.Z, Pauli.Z])\n",
+    "        qpo_dict[term_string] = -0.5*cost_angle\n",
+    "    return QubitPauliOperator(qpo_dict)\n",
+    "\n",
+    "cost_angle = 1.0\n",
+    "cost_ham_qpo = qaoa_graph_to_cost_hamiltonian(max_cut_graph_edges, cost_angle)\n",
+    "print(cost_ham_qpo)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6da499ac",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "fragment"
+    }
+   },
+   "source": [
+    "$$\n",
+    "\\begin{equation}\n",
+    "H_P = 3 I^{\\otimes 6} -0.5 \\big[ Z_0 Z_1 + Z_1 Z_2 +Z_1 Z_3 +Z_3 Z_4 +Z_4 Z_5 +Z_4 Z_6  \\big]\n",
+    "\\end{equation}\n",
+    "$$\n",
+    "\n",
+    "Using the same index convention as above"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "785ff56c",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "slide"
+    }
+   },
+   "source": [
+    "## Hamiltonian Circuit"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "11fe9917",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "fragment"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "from pytket.utils import gen_term_sequence_circuit\n",
+    "from pytket import Circuit\n",
+    "from pytket.circuit import display\n",
+    "\n",
+    "cost_ham_circuit = gen_term_sequence_circuit(cost_ham_qpo, Circuit(n_nodes))\n",
+    "display.render_circuit_jupyter(cost_ham_circuit)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "9057c55f",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "slide"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "from pytket.transform import Transform\n",
+    "\n",
+    "Transform.DecomposeBoxes().apply(cost_ham_circuit)\n",
+    "display.render_circuit_jupyter(cost_ham_circuit)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4690b787",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "slide"
+    }
+   },
+   "source": [
+    "## Construction of the Mixer Hamiltonian: $\\beta B$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "296c560d",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "fragment"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "mixer_angle = 0.8\n",
+    "mixer_ham_qpo =  QubitPauliOperator({QubitPauliString([Qubit(i)], [Pauli.X]): mixer_angle for i in range(n_nodes)})\n",
+    "mixer_ham_circuit = gen_term_sequence_circuit(mixer_ham_qpo, Circuit(n_nodes))\n",
+    "Transform.DecomposeBoxes().apply(mixer_ham_circuit)\n",
+    "display.render_circuit_jupyter(mixer_ham_circuit)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4d128a70",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "slide"
+    }
+   },
+   "source": [
+    "## Define the Initial State"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "0a9db628",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "fragment"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "def qaoa_initial_circuit(n_qubits: int) -> Circuit:\n",
+    "    c = Circuit(n_qubits)\n",
+    "    for i in range(n_qubits):\n",
+    "        c.H(i)\n",
+    "    return c\n",
+    "\n",
+    "superposition_circuit = qaoa_initial_circuit(n_nodes)\n",
+    "\n",
+    "display.render_circuit_jupyter(superposition_circuit)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "da759b59",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "slide"
+    }
+   },
+   "source": [
+    "## Construct QAOA Circuit"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "359a1a0f-e92e-40ae-bbe6-ce960b118f49",
+   "metadata": {},
+   "source": [
+    "Now lets define a function to create our entire QAOA circuit. For $p$ QAOA layers we expect that our circuit will require $2p$ parameters. Here we will pass and cost mixer parameters in as a list where the length of the list defines the number of layers."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "id": "23f8910a",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "fragment"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "def qaoa_max_cut_circuit(edges: List[Tuple[int, int]],\n",
+    "                         n_nodes: int,\n",
+    "                         mixer_angles: List[float],\n",
+    "                         cost_angles: List[float]) -> Circuit:\n",
+    "    \n",
+    "    assert len(mixer_angles) == len(cost_angles)\n",
+    "    \n",
+    "    # initial state\n",
+    "    qaoa_circuit = qaoa_initial_circuit(n_nodes)\n",
+    "    \n",
+    "    # add cost and mixer terms to state\n",
+    "    for cost, mixer in zip(cost_angles, mixer_angles):\n",
+    "        cost_ham = qaoa_graph_to_cost_hamiltonian(edges, cost)\n",
+    "        mixer_ham = QubitPauliOperator({QubitPauliString([Qubit(i)], [Pauli.X]): mixer for i in range(n_nodes)})\n",
+    "        qaoa_circuit.append(gen_term_sequence_circuit(cost_ham, Circuit(n_nodes)))\n",
+    "        qaoa_circuit.append(gen_term_sequence_circuit(mixer_ham, Circuit(n_nodes)))\n",
+    "        \n",
+    "    Transform.DecomposeBoxes().apply(qaoa_circuit)\n",
+    "    return qaoa_circuit"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "bc2f8939-41b7-476b-a5a8-09de07211079",
+   "metadata": {},
+   "source": [
+    "We also need to extract our energy expectation values from a `BackendResult` object after our circuit is processed by the device/simulator. We do this with the `get_max_cut_energy` function below. Note that the fact that the maxcut Hamiltonian contains only commuting terms means that we do not need to calculate our energy expectation using multiple measurement circuits. This may not the the case for a different problem Hamiltonian."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "id": "df387eea-4198-428e-9b92-4f3bceb12f0e",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from typing import List, Tuple\n",
+    "from pytket.backends.backendresult import BackendResult\n",
+    "\n",
+    "def get_max_cut_energy(edges: List[Tuple[int, int]], results: BackendResult) -> float:\n",
+    "    energy = 0.0\n",
+    "    dist = results.get_distribution()\n",
+    "    for i, j in edges:\n",
+    "        energy += sum((meas[i] ^ meas[j]) * prob for meas, prob in dist.items())\n",
+    "\n",
+    "    return energy"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "id": "e5abad7b-e989-4156-9708-3d8c97d8ca2a",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from pytket.backends.backend import Backend\n",
+    "from typing import Callable\n",
+    "import numpy as np\n",
+    "\n",
+    "def qaoa_instance(\n",
+    "    backend: Backend,\n",
+    "    compiler_pass: Callable[[Circuit], bool],\n",
+    "    guess_mixer_angles: np.array,\n",
+    "    guess_cost_angles: np.array,\n",
+    "    seed: int,\n",
+    "    shots: int = 5000,\n",
+    ") -> float:\n",
+    "    # step 1: get state guess\n",
+    "    my_prep_circuit = qaoa_max_cut_circuit(\n",
+    "        max_cut_graph_edges, n_nodes, guess_mixer_angles, guess_cost_angles\n",
+    "    )\n",
+    "    measured_circ = my_prep_circuit.copy().measure_all()\n",
+    "    compiler_pass(measured_circ)\n",
+    "    res = backend.run_circuit(measured_circ, shots, seed=seed)\n",
+    "\n",
+    "    return get_max_cut_energy(max_cut_graph_edges, res)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2c01c28b",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "slide"
+    }
+   },
+   "source": [
+    "## Optimise Energy by Guessing Parameters"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "id": "0a44bed8",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "fragment"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "def qaoa_optimise_energy(compiler_pass: Callable[[Circuit], bool],\n",
+    "                         backend: Backend,\n",
+    "                         iterations: int = 100,\n",
+    "                         n: int = 3,\n",
+    "                         shots: int = 5000,\n",
+    "                         seed: int= 12345):\n",
+    "    \n",
+    "    highest_energy = 0    \n",
+    "    best_guess_mixer_angles = [0 for i in range(n)]    \n",
+    "    best_guess_cost_angles = [0 for i in range(n)]\n",
+    "    rng = np.random.default_rng(seed)\n",
+    "    # guess some angles (iterations)-times and try if they are better than the best angles found before\n",
+    "    \n",
+    "    for i in range(iterations):\n",
+    "        \n",
+    "        guess_mixer_angles = rng.uniform(0, 1, n)\n",
+    "        guess_cost_angles = rng.uniform(0, 1, n)\n",
+    "        \n",
+    "        qaoa_energy = qaoa_instance(backend,\n",
+    "                                    compiler_pass,\n",
+    "                                    guess_mixer_angles,\n",
+    "                                    guess_cost_angles,\n",
+    "                                    seed=seed,\n",
+    "                                    shots=shots)\n",
+    "        \n",
+    "        if(qaoa_energy > highest_energy):\n",
+    "            \n",
+    "            print(\"new highest energy found: \", qaoa_energy)\n",
+    "            \n",
+    "            best_guess_mixer_angles = np.round(guess_mixer_angles, 3)\n",
+    "            best_guess_cost_angles = np.round(guess_cost_angles, 3)\n",
+    "            highest_energy = qaoa_energy\n",
+    "            \n",
+    "    print(\"highest energy: \", highest_energy)\n",
+    "    print(\"best guess mixer angles: \", best_guess_mixer_angles)\n",
+    "    print(\"best guess cost angles: \", best_guess_cost_angles)\n",
+    "    return best_guess_mixer_angles, best_guess_cost_angles"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d22226cc",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "slide"
+    }
+   },
+   "source": [
+    "## Calculate the State for the final Parameters"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "id": "da46e63d",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "fragment"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "def qaoa_calculate(backend: Backend,\n",
+    "                   compiler_pass: Callable[[Circuit], bool],\n",
+    "                   shots: int = 5000,\n",
+    "                   iterations: int = 100,\n",
+    "                   seed: int = 12345,\n",
+    "                  ) -> BackendResult:\n",
+    "    \n",
+    "    # find the parameters for the highest energy\n",
+    "    best_mixer, best_cost = qaoa_optimise_energy(compiler_pass,\n",
+    "                                                 backend,\n",
+    "                                                 iterations,\n",
+    "                                                 3,\n",
+    "                                                 shots=shots,\n",
+    "                                                 seed=seed)\n",
+    "    \n",
+    "    # get the circuit with the final parameters of the optimisation:\n",
+    "    my_qaoa_circuit = qaoa_max_cut_circuit(max_cut_graph_edges,\n",
+    "                                           n_nodes,\n",
+    "                                           best_mixer,\n",
+    "                                           best_cost)\n",
+    "\n",
+    "    my_qaoa_circuit.measure_all()\n",
+    "\n",
+    "    compiler_pass(my_qaoa_circuit)\n",
+    "    handle = backend.process_circuit(my_qaoa_circuit, shots, seed=seed)\n",
+    "\n",
+    "    result = backend.get_result(handle)    \n",
+    "    \n",
+    "    return result"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9dd97e10",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "slide"
+    }
+   },
+   "source": [
+    "## Results with the Noiseless Simulator"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "id": "e7afb38e",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "fragment"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "from pytket.extensions.qiskit import AerBackend\n",
+    "\n",
+    "backend = AerBackend()\n",
+    "comp = backend.get_compiled_circuit"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "aaea7e2f",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "slide"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "%%time\n",
+    "res = qaoa_calculate(backend, backend.default_compilation_pass(2).apply, shots = 5000, iterations = 100, seed=12345)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "3b86301e-7645-4553-be38-3ebf89eedd37",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from maxcut_plotting import plot_maxcut_results\n",
+    "\n",
+    "plot_maxcut_results(res, 6)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6e36c4fb-a118-4ab8-be01-77a674f273e3",
+   "metadata": {},
+   "source": [
+    "Here the binary strings in the results correspond to the two optimal colourings of our graph."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "ffce2a97-902c-44d8-8d64-b25498752907",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "G = nx.Graph()\n",
+    "G.add_edges_from(max_cut_graph_edges)\n",
+    "\n",
+    "H = nx.Graph()\n",
+    "H.add_edges_from(max_cut_graph_edges)\n",
+    "\n",
+    "plt.figure(1)\n",
+    "nx.draw(G, labels={node: node for node in max_cut_graph.nodes()}, node_color= ['red', 'blue', 'red','red', 'blue', 'red', 'red'])\n",
+    "plt.figure(2)\n",
+    "nx.draw(H, labels={node: node for node in max_cut_graph.nodes()}, node_color= ['blue', 'red', 'blue', 'blue', 'red', 'blue', 'blue'])\n",
+    "\n",
+    "plt.show()"
+   ]
+  }
+ ],
+ "metadata": {
+  "celltoolbar": "Slideshow",
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.11.1"
+  },
+  "vscode": {
+   "interpreter": {
+    "hash": "3289aa74b4cc5b65254d7b081e6c83acb4efa1b1c1d2fe845644451ee4b44b02"
+   }
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}

From 8af8e188865c0c411de8e42680d121e30e2a9508 Mon Sep 17 00:00:00 2001
From: CalMacCQ <93673602+CalMacCQ@users.noreply.github.com>
Date: Thu, 19 Dec 2024 15:23:14 +0000
Subject: [PATCH 02/17] cleanup QAOA example some more

---
 .../pytket_qaoa_maxcut_example.ipynb          | 51 +++++++++++++++----
 1 file changed, 41 insertions(+), 10 deletions(-)

diff --git a/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb b/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb
index 924ae35d..6cc3a857 100644
--- a/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb
+++ b/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb
@@ -9,7 +9,7 @@
     }
    },
    "source": [
-    "# The Quantum Approximate Optimisation Algorithm (QAOA) using TKET."
+    "# Quantum approximate optimisation algorithm (QAOA) applied to maxcut."
    ]
   },
   {
@@ -76,10 +76,13 @@
     "$$\n",
     "| \\psi  ( \\beta, \\gamma ) \\rangle = U ( \\beta_m ) U ( \\gamma_m ) ... U (\\beta_0) U ( \\gamma_0 ) | \\psi_0 \\rangle\n",
     "$$\n",
+    "\n",
     "where\n",
+    "\n",
     "$$\n",
     "U( \\beta_i ) = e^{i \\beta H_B} \\quad \\& \\quad U ( \\gamma_i) = e^{i \\gamma H_P}\n",
     "$$\n",
+    "\n",
     "with $H_P$ depending on the problem instance. "
    ]
   },
@@ -106,6 +109,7 @@
    },
    "source": [
     "For the previous 3 vertex graph the *problem Hamiltonian* is\n",
+    "\n",
     "$$\n",
     "H_P = \\frac{1}{2} \\Big[ ( Z \\otimes Z \\otimes I ) + ( Z \\otimes I \\otimes Z ) + ( I \\otimes Z \\otimes Z ) \\Big]\n",
     "$$\n",
@@ -123,6 +127,7 @@
    },
    "source": [
     "The *mixer Hamiltonian* has the form \n",
+    "\n",
     "$$\n",
     "H_B =   ( X \\otimes I \\otimes I ) + ( I \\otimes X \\otimes I ) + ( I \\otimes I \\otimes X )\n",
     "$$\n",
@@ -263,7 +268,7 @@
    "source": [
     "$$\n",
     "\\begin{equation}\n",
-    "H_P = \\frac{1}{2}\\sum_{<jk>} (-Z_j \\,Z_k +I )\n",
+    "H_P = \\frac{1}{2}\\sum_{(i, \\, j)} (I -Z_i \\,Z_j)\n",
     "\\end{equation}\n",
     "$$"
    ]
@@ -280,12 +285,11 @@
    },
    "outputs": [],
    "source": [
-    "from typing import List, Tuple, Any\n",
     "from pytket.utils import QubitPauliOperator\n",
     "from pytket.pauli import QubitPauliString, Pauli\n",
     "from pytket import Qubit\n",
     "\n",
-    "def qaoa_graph_to_cost_hamiltonian(edges: List[Tuple[int, int]], cost_angle: float) -> QubitPauliOperator:\n",
+    "def qaoa_graph_to_cost_hamiltonian(edges: list[tuple[int, int]], cost_angle: float) -> QubitPauliOperator:\n",
     "    qpo_dict = {QubitPauliString(): len(edges)*0.5*cost_angle}\n",
     "    for e in edges:\n",
     "        term_string = QubitPauliString([Qubit(e[0]), Qubit(e[1])], [Pauli.Z, Pauli.Z])\n",
@@ -458,10 +462,10 @@
    },
    "outputs": [],
    "source": [
-    "def qaoa_max_cut_circuit(edges: List[Tuple[int, int]],\n",
+    "def qaoa_max_cut_circuit(edges: list[tuple[int, int]],\n",
     "                         n_nodes: int,\n",
-    "                         mixer_angles: List[float],\n",
-    "                         cost_angles: List[float]) -> Circuit:\n",
+    "                         mixer_angles: list[float],\n",
+    "                         cost_angles: list[float]) -> Circuit:\n",
     "    \n",
     "    assert len(mixer_angles) == len(cost_angles)\n",
     "    \n",
@@ -494,10 +498,9 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "from typing import List, Tuple\n",
     "from pytket.backends.backendresult import BackendResult\n",
     "\n",
-    "def get_max_cut_energy(edges: List[Tuple[int, int]], results: BackendResult) -> float:\n",
+    "def get_max_cut_energy(edges: list[tuple[int, int]], results: BackendResult) -> float:\n",
     "    energy = 0.0\n",
     "    dist = results.get_distribution()\n",
     "    for i, j in edges:\n",
@@ -703,7 +706,35 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "from maxcut_plotting import plot_maxcut_results\n",
+    "import matplotlib.pyplot as plt\n",
+    "\n",
+    "def plot_maxcut_results(result: BackendResult, n_strings: int) -> None:\n",
+    "    \"\"\"\n",
+    "    Plots Maxcut results in a barchart with the two most common bitstrings highlighted in green.\n",
+    "    \"\"\"\n",
+    "    counts_dict = result.get_counts()\n",
+    "    sorted_shots = counts_dict.most_common()\n",
+    "    n_shots = sum(counts_dict.values())\n",
+    "\n",
+    "    n_most_common_strings = sorted_shots[:n_strings]\n",
+    "    x_axis_values = [str(entry[0]) for entry in n_most_common_strings]  # basis states\n",
+    "    y_axis_values = [entry[1] for entry in n_most_common_strings]  # counts\n",
+    "    num_successful_shots = sum(y_axis_values[:2])\n",
+    "    print(f\"Success ratio {num_successful_shots/n_shots} \")\n",
+    "\n",
+    "    fig = plt.figure()\n",
+    "    ax = fig.add_axes([0, 0, 1.5, 1])\n",
+    "    color_list = [\"green\"] * 2 + ([\"orange\"] * (len(x_axis_values) - 2))\n",
+    "    ax.bar(\n",
+    "        x=x_axis_values,\n",
+    "        height=y_axis_values,\n",
+    "        color=color_list,\n",
+    "    )\n",
+    "    ax.set_title(label=\"Maxcut Results\")\n",
+    "    plt.ylim([0, 0.25 * n_shots])\n",
+    "    plt.xlabel(\"Basis State\")\n",
+    "    plt.ylabel(\"Number of Shots\")\n",
+    "    plt.show()\n",
     "\n",
     "plot_maxcut_results(res, 6)"
    ]

From a811437f5a8a468b4d0d3b3f09c64e83c9312cff Mon Sep 17 00:00:00 2001
From: CalMacCQ <93673602+CalMacCQ@users.noreply.github.com>
Date: Mon, 23 Dec 2024 18:47:07 +0000
Subject: [PATCH 03/17] refactor circuit builders

---
 .../pytket_qaoa_maxcut_example.ipynb          | 401 +++++++++++-------
 1 file changed, 255 insertions(+), 146 deletions(-)

diff --git a/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb b/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb
index 6cc3a857..6963db67 100644
--- a/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb
+++ b/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb
@@ -26,14 +26,25 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 1,
    "id": "9456fbeb",
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
     }
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "image/png": "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",
+      "text/plain": [
+       "<Figure size 200x200 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "import networkx as nx\n",
     "import matplotlib.pyplot as plt\n",
@@ -228,14 +239,25 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 3,
    "id": "688f1332",
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
     }
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "import networkx as nx\n",
     "\n",
@@ -273,34 +295,6 @@
     "$$"
    ]
   },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "99226b24",
-   "metadata": {
-    "scrolled": true,
-    "slideshow": {
-     "slide_type": "fragment"
-    }
-   },
-   "outputs": [],
-   "source": [
-    "from pytket.utils import QubitPauliOperator\n",
-    "from pytket.pauli import QubitPauliString, Pauli\n",
-    "from pytket import Qubit\n",
-    "\n",
-    "def qaoa_graph_to_cost_hamiltonian(edges: list[tuple[int, int]], cost_angle: float) -> QubitPauliOperator:\n",
-    "    qpo_dict = {QubitPauliString(): len(edges)*0.5*cost_angle}\n",
-    "    for e in edges:\n",
-    "        term_string = QubitPauliString([Qubit(e[0]), Qubit(e[1])], [Pauli.Z, Pauli.Z])\n",
-    "        qpo_dict[term_string] = -0.5*cost_angle\n",
-    "    return QubitPauliOperator(qpo_dict)\n",
-    "\n",
-    "cost_angle = 1.0\n",
-    "cost_ham_qpo = qaoa_graph_to_cost_hamiltonian(max_cut_graph_edges, cost_angle)\n",
-    "print(cost_ham_qpo)"
-   ]
-  },
   {
    "cell_type": "markdown",
    "id": "6da499ac",
@@ -331,42 +325,6 @@
     "## Hamiltonian Circuit"
    ]
   },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "11fe9917",
-   "metadata": {
-    "slideshow": {
-     "slide_type": "fragment"
-    }
-   },
-   "outputs": [],
-   "source": [
-    "from pytket.utils import gen_term_sequence_circuit\n",
-    "from pytket import Circuit\n",
-    "from pytket.circuit import display\n",
-    "\n",
-    "cost_ham_circuit = gen_term_sequence_circuit(cost_ham_qpo, Circuit(n_nodes))\n",
-    "display.render_circuit_jupyter(cost_ham_circuit)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "9057c55f",
-   "metadata": {
-    "slideshow": {
-     "slide_type": "slide"
-    }
-   },
-   "outputs": [],
-   "source": [
-    "from pytket.transform import Transform\n",
-    "\n",
-    "Transform.DecomposeBoxes().apply(cost_ham_circuit)\n",
-    "display.render_circuit_jupyter(cost_ham_circuit)"
-   ]
-  },
   {
    "cell_type": "markdown",
    "id": "4690b787",
@@ -379,24 +337,6 @@
     "## Construction of the Mixer Hamiltonian: $\\beta B$"
    ]
   },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "296c560d",
-   "metadata": {
-    "slideshow": {
-     "slide_type": "fragment"
-    }
-   },
-   "outputs": [],
-   "source": [
-    "mixer_angle = 0.8\n",
-    "mixer_ham_qpo =  QubitPauliOperator({QubitPauliString([Qubit(i)], [Pauli.X]): mixer_angle for i in range(n_nodes)})\n",
-    "mixer_ham_circuit = gen_term_sequence_circuit(mixer_ham_qpo, Circuit(n_nodes))\n",
-    "Transform.DecomposeBoxes().apply(mixer_ham_circuit)\n",
-    "display.render_circuit_jupyter(mixer_ham_circuit)"
-   ]
-  },
   {
    "cell_type": "markdown",
    "id": "4d128a70",
@@ -411,15 +351,97 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 20,
    "id": "0a9db628",
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
     }
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "\n",
+       "\n",
+       "\n",
+       "\n",
+       "\n",
+       "\n",
+       "<div style=\"resize: vertical; overflow: auto; height: 300px; display: block\">\n",
+       "    <iframe srcdoc=\"\n",
+       "&lt;!DOCTYPE html&gt;\n",
+       "&lt;html lang=&#34;en&#34;&gt;\n",
+       "&lt;head&gt;\n",
+       "    &lt;meta charset=&#34;UTF-8&#34;&gt;\n",
+       "    &lt;!-- Download Vue 3--&gt;\n",
+       "&lt;script type=&#34;application/javascript&#34; src=&#34;https://cdn.jsdelivr.net/npm/vue@3&#34;&gt;&lt;/script&gt;\n",
+       "&lt;!-- Download Circuit Renderer with styles --&gt;\n",
+       "&lt;script type=&#34;application/javascript&#34; src=&#34;https://unpkg.com/pytket-circuit-renderer@0.10/dist/pytket-circuit-renderer.umd.js&#34;&gt;&lt;/script&gt;\n",
+       "&lt;link rel=&#34;stylesheet&#34; href=&#34;https://unpkg.com/pytket-circuit-renderer@0.10/dist/pytket-circuit-renderer.css&#34;&gt;\n",
+       "&lt;/head&gt;\n",
+       "&lt;body&gt;\n",
+       "\n",
+       "\n",
+       "    &lt;div id=&#34;circuit-display-vue-container-263764c6-112b-478e-b136-309e5b359aea&#34; class=&#34;pytket-circuit-display-container&#34;&gt;\n",
+       "        &lt;div style=&#34;display: none&#34;&gt;\n",
+       "            &lt;div id=&#34;circuit-json-to-display&#34;&gt;{&#34;bits&#34;: [], &#34;commands&#34;: [{&#34;args&#34;: [[&#34;q&#34;, [0]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [1]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [2]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [3]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [4]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [5]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [6]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}], &#34;created_qubits&#34;: [], &#34;discarded_qubits&#34;: [], &#34;implicit_permutation&#34;: [[[&#34;q&#34;, [0]], [&#34;q&#34;, [0]]], [[&#34;q&#34;, [1]], [&#34;q&#34;, [1]]], [[&#34;q&#34;, [2]], [&#34;q&#34;, [2]]], [[&#34;q&#34;, [3]], [&#34;q&#34;, [3]]], [[&#34;q&#34;, [4]], [&#34;q&#34;, [4]]], [[&#34;q&#34;, [5]], [&#34;q&#34;, [5]]], [[&#34;q&#34;, [6]], [&#34;q&#34;, [6]]]], &#34;phase&#34;: &#34;0.0&#34;, &#34;qubits&#34;: [[&#34;q&#34;, [0]], [&#34;q&#34;, [1]], [&#34;q&#34;, [2]], [&#34;q&#34;, [3]], [&#34;q&#34;, [4]], [&#34;q&#34;, [5]], [&#34;q&#34;, [6]]]}&lt;/div&gt;\n",
+       "        &lt;/div&gt;\n",
+       "        &lt;circuit-display-container\n",
+       "                :circuit-element-str=&#34;&#39;#circuit-json-to-display&#39;&#34;\n",
+       "                :init-render-options=&#34;initRenderOptions&#34;\n",
+       "                view-format=&#34;None&#34;\n",
+       "        &gt;&lt;/circuit-display-container&gt;\n",
+       "    &lt;/div&gt;\n",
+       "    &lt;script type=&#34;application/javascript&#34;&gt;\n",
+       "      const circuitRendererUid = &#34;263764c6-112b-478e-b136-309e5b359aea&#34;;\n",
+       "      const displayOptions = JSON.parse(&#39;{&#34;zxStyle&#34;: true, &#34;condenseCBits&#34;: false}&#39;);\n",
+       "\n",
+       "      // Script to initialise the circuit renderer app\n",
+       "\n",
+       "const { createApp } = Vue;\n",
+       "const circuitDisplayContainer = window[&#34;pytket-circuit-renderer&#34;].default;\n",
+       "// Init variables to be shared between circuit display instances\n",
+       "if (typeof window.pytketCircuitDisplays === &#34;undefined&#34;) {\n",
+       "    window.pytketCircuitDisplays = {};\n",
+       "}\n",
+       "// Create the root Vue component\n",
+       "const app = createApp({\n",
+       "    delimiters: [&#39;[[#&#39;, &#39;#]]&#39;],\n",
+       "    components: { circuitDisplayContainer },\n",
+       "    data () {\n",
+       "      return {\n",
+       "        initRenderOptions: displayOptions,\n",
+       "      }\n",
+       "    }\n",
+       "})\n",
+       "app.config.unwrapInjectedRef = true;\n",
+       "app.mount(&#34;#circuit-display-vue-container-&#34;+circuitRendererUid);\n",
+       "window.pytketCircuitDisplays[circuitRendererUid] = app;\n",
+       "    &lt;/script&gt;\n",
+       "\n",
+       "\n",
+       "\n",
+       "&lt;/body&gt;\n",
+       "&lt;/html&gt;\n",
+       "\"\n",
+       "            width=\"100%\" height=\"100%\"\n",
+       "            style=\"border: none; outline: none; overflow: auto\"></iframe>\n",
+       "</div>\n",
+       "\n"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
+    "from pytket import Circuit\n",
+    "from pytket.circuit.display import render_circuit_jupyter as draw\n",
+    "\n",
     "def qaoa_initial_circuit(n_qubits: int) -> Circuit:\n",
     "    c = Circuit(n_qubits)\n",
     "    for i in range(n_qubits):\n",
@@ -428,7 +450,7 @@
     "\n",
     "superposition_circuit = qaoa_initial_circuit(n_nodes)\n",
     "\n",
-    "display.render_circuit_jupyter(superposition_circuit)"
+    "draw(superposition_circuit)"
    ]
   },
   {
@@ -443,6 +465,40 @@
     "## Construct QAOA Circuit"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "id": "57c9ed7e",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from pytket import Circuit\n",
+    "\n",
+    "def build_cost_layer(graph: nx.Graph, gamma_val: float) -> Circuit:\n",
+    "    circ = Circuit(graph.number_of_nodes())\n",
+    "    \n",
+    "    for i, j in list(graph.edges):\n",
+    "        circ.ZZPhase(gamma_val, i, j)\n",
+    "\n",
+    "    return circ\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "id": "5f43f97a",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def build_mixer_layer(n_vertices: int, beta_val: float) -> Circuit:\n",
+    "    circ = Circuit(n_vertices)\n",
+    "\n",
+    "    for qubit in circ.qubits:\n",
+    "        circ.Rx(beta_val, qubit)\n",
+    "\n",
+    "    return circ"
+   ]
+  },
   {
    "cell_type": "markdown",
    "id": "359a1a0f-e92e-40ae-bbe6-ce960b118f49",
@@ -453,7 +509,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 11,
    "id": "23f8910a",
    "metadata": {
     "slideshow": {
@@ -462,24 +518,20 @@
    },
    "outputs": [],
    "source": [
-    "def qaoa_max_cut_circuit(edges: list[tuple[int, int]],\n",
-    "                         n_nodes: int,\n",
-    "                         mixer_angles: list[float],\n",
-    "                         cost_angles: list[float]) -> Circuit:\n",
-    "    \n",
+    "def qaoa_max_cut_circuit(\n",
+    "    graph: nx.Graph, n_nodes: int, mixer_angles: list[float], cost_angles: list[float]\n",
+    ") -> Circuit:\n",
+    "\n",
     "    assert len(mixer_angles) == len(cost_angles)\n",
-    "    \n",
-    "    # initial state\n",
+    "\n",
+    "    # Start from the uniform superposition state\n",
     "    qaoa_circuit = qaoa_initial_circuit(n_nodes)\n",
-    "    \n",
+    "\n",
     "    # add cost and mixer terms to state\n",
     "    for cost, mixer in zip(cost_angles, mixer_angles):\n",
-    "        cost_ham = qaoa_graph_to_cost_hamiltonian(edges, cost)\n",
-    "        mixer_ham = QubitPauliOperator({QubitPauliString([Qubit(i)], [Pauli.X]): mixer for i in range(n_nodes)})\n",
-    "        qaoa_circuit.append(gen_term_sequence_circuit(cost_ham, Circuit(n_nodes)))\n",
-    "        qaoa_circuit.append(gen_term_sequence_circuit(mixer_ham, Circuit(n_nodes)))\n",
-    "        \n",
-    "    Transform.DecomposeBoxes().apply(qaoa_circuit)\n",
+    "        qaoa_circuit.append(build_cost_layer(graph, cost))\n",
+    "        qaoa_circuit.append(build_mixer_layer(n_nodes, mixer))\n",
+    "\n",
     "    return qaoa_circuit"
    ]
   },
@@ -493,7 +545,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 12,
    "id": "df387eea-4198-428e-9b92-4f3bceb12f0e",
    "metadata": {},
    "outputs": [],
@@ -511,7 +563,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 13,
    "id": "e5abad7b-e989-4156-9708-3d8c97d8ca2a",
    "metadata": {},
    "outputs": [],
@@ -530,7 +582,7 @@
     ") -> float:\n",
     "    # step 1: get state guess\n",
     "    my_prep_circuit = qaoa_max_cut_circuit(\n",
-    "        max_cut_graph_edges, n_nodes, guess_mixer_angles, guess_cost_angles\n",
+    "        max_cut_graph, n_nodes, guess_mixer_angles, guess_cost_angles\n",
     "    )\n",
     "    measured_circ = my_prep_circuit.copy().measure_all()\n",
     "    compiler_pass(measured_circ)\n",
@@ -553,7 +605,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 14,
    "id": "0a44bed8",
    "metadata": {
     "slideshow": {
@@ -562,39 +614,43 @@
    },
    "outputs": [],
    "source": [
-    "def qaoa_optimise_energy(compiler_pass: Callable[[Circuit], bool],\n",
-    "                         backend: Backend,\n",
-    "                         iterations: int = 100,\n",
-    "                         n: int = 3,\n",
-    "                         shots: int = 5000,\n",
-    "                         seed: int= 12345):\n",
-    "    \n",
-    "    highest_energy = 0    \n",
-    "    best_guess_mixer_angles = [0 for i in range(n)]    \n",
+    "def qaoa_optimise_energy(\n",
+    "    compiler_pass: Callable[[Circuit], bool],\n",
+    "    backend: Backend,\n",
+    "    iterations: int = 100,\n",
+    "    n: int = 3,\n",
+    "    shots: int = 5000,\n",
+    "    seed: int = 12345,\n",
+    "):\n",
+    "\n",
+    "    highest_energy = 0\n",
+    "    best_guess_mixer_angles = [0 for i in range(n)]\n",
     "    best_guess_cost_angles = [0 for i in range(n)]\n",
     "    rng = np.random.default_rng(seed)\n",
     "    # guess some angles (iterations)-times and try if they are better than the best angles found before\n",
-    "    \n",
+    "\n",
     "    for i in range(iterations):\n",
-    "        \n",
+    "\n",
     "        guess_mixer_angles = rng.uniform(0, 1, n)\n",
     "        guess_cost_angles = rng.uniform(0, 1, n)\n",
-    "        \n",
-    "        qaoa_energy = qaoa_instance(backend,\n",
-    "                                    compiler_pass,\n",
-    "                                    guess_mixer_angles,\n",
-    "                                    guess_cost_angles,\n",
-    "                                    seed=seed,\n",
-    "                                    shots=shots)\n",
-    "        \n",
-    "        if(qaoa_energy > highest_energy):\n",
-    "            \n",
+    "\n",
+    "        qaoa_energy = qaoa_instance(\n",
+    "            backend,\n",
+    "            compiler_pass,\n",
+    "            guess_mixer_angles,\n",
+    "            guess_cost_angles,\n",
+    "            seed=seed,\n",
+    "            shots=shots,\n",
+    "        )\n",
+    "\n",
+    "        if qaoa_energy > highest_energy:\n",
+    "\n",
     "            print(\"new highest energy found: \", qaoa_energy)\n",
-    "            \n",
+    "\n",
     "            best_guess_mixer_angles = np.round(guess_mixer_angles, 3)\n",
     "            best_guess_cost_angles = np.round(guess_cost_angles, 3)\n",
     "            highest_energy = qaoa_energy\n",
-    "            \n",
+    "\n",
     "    print(\"highest energy: \", highest_energy)\n",
     "    print(\"best guess mixer angles: \", best_guess_mixer_angles)\n",
     "    print(\"best guess cost angles: \", best_guess_cost_angles)\n",
@@ -615,7 +671,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 15,
    "id": "da46e63d",
    "metadata": {
     "slideshow": {
@@ -640,7 +696,7 @@
     "                                                 seed=seed)\n",
     "    \n",
     "    # get the circuit with the final parameters of the optimisation:\n",
-    "    my_qaoa_circuit = qaoa_max_cut_circuit(max_cut_graph_edges,\n",
+    "    my_qaoa_circuit = qaoa_max_cut_circuit(max_cut_graph,\n",
     "                                           n_nodes,\n",
     "                                           best_mixer,\n",
     "                                           best_cost)\n",
@@ -669,7 +725,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 16,
    "id": "e7afb38e",
    "metadata": {
     "slideshow": {
@@ -686,14 +742,33 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 17,
    "id": "aaea7e2f",
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
     }
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "new highest energy found:  2.8042\n",
+      "new highest energy found:  3.2636000000000003\n",
+      "new highest energy found:  3.570399999999999\n",
+      "new highest energy found:  3.6372000000000004\n",
+      "new highest energy found:  4.073799999999999\n",
+      "new highest energy found:  4.356799999999999\n",
+      "new highest energy found:  4.467\n",
+      "highest energy:  4.467\n",
+      "best guess mixer angles:  [0.597 0.742 0.064]\n",
+      "best guess cost angles:  [0.165 0.353 0.249]\n",
+      "CPU times: user 2min 15s, sys: 34.1 s, total: 2min 49s\n",
+      "Wall time: 42.3 s\n"
+     ]
+    }
+   ],
    "source": [
     "%%time\n",
     "res = qaoa_calculate(backend, backend.default_compilation_pass(2).apply, shots = 5000, iterations = 100, seed=12345)"
@@ -701,10 +776,28 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 18,
    "id": "3b86301e-7645-4553-be38-3ebf89eedd37",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Success ratio 0.202 \n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "import matplotlib.pyplot as plt\n",
     "\n",
@@ -749,10 +842,31 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 19,
    "id": "ffce2a97-902c-44d8-8d64-b25498752907",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "G = nx.Graph()\n",
     "G.add_edges_from(max_cut_graph_edges)\n",
@@ -772,7 +886,7 @@
  "metadata": {
   "celltoolbar": "Slideshow",
   "kernelspec": {
-   "display_name": "Python 3 (ipykernel)",
+   "display_name": ".venv",
    "language": "python",
    "name": "python3"
   },
@@ -787,11 +901,6 @@
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
    "version": "3.11.1"
-  },
-  "vscode": {
-   "interpreter": {
-    "hash": "3289aa74b4cc5b65254d7b081e6c83acb4efa1b1c1d2fe845644451ee4b44b02"
-   }
   }
  },
  "nbformat": 4,

From 258b9f1300997ccb3bebad918f6f41bb8087bd1a Mon Sep 17 00:00:00 2001
From: CalMacCQ <93673602+CalMacCQ@users.noreply.github.com>
Date: Mon, 23 Dec 2024 18:47:52 +0000
Subject: [PATCH 04/17] clear outputs

---
 .../pytket_qaoa_maxcut_example.ipynb          | 183 ++----------------
 1 file changed, 12 insertions(+), 171 deletions(-)

diff --git a/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb b/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb
index 6963db67..985cf29d 100644
--- a/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb
+++ b/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb
@@ -26,25 +26,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": null,
    "id": "9456fbeb",
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
     }
    },
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "<Figure size 200x200 with 1 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "import networkx as nx\n",
     "import matplotlib.pyplot as plt\n",
@@ -239,25 +228,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": null,
    "id": "688f1332",
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
     }
    },
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "import networkx as nx\n",
     "\n",
@@ -351,93 +329,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 20,
+   "execution_count": null,
    "id": "0a9db628",
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
     }
    },
-   "outputs": [
-    {
-     "data": {
-      "text/html": [
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "<div style=\"resize: vertical; overflow: auto; height: 300px; display: block\">\n",
-       "    <iframe srcdoc=\"\n",
-       "&lt;!DOCTYPE html&gt;\n",
-       "&lt;html lang=&#34;en&#34;&gt;\n",
-       "&lt;head&gt;\n",
-       "    &lt;meta charset=&#34;UTF-8&#34;&gt;\n",
-       "    &lt;!-- Download Vue 3--&gt;\n",
-       "&lt;script type=&#34;application/javascript&#34; src=&#34;https://cdn.jsdelivr.net/npm/vue@3&#34;&gt;&lt;/script&gt;\n",
-       "&lt;!-- Download Circuit Renderer with styles --&gt;\n",
-       "&lt;script type=&#34;application/javascript&#34; src=&#34;https://unpkg.com/pytket-circuit-renderer@0.10/dist/pytket-circuit-renderer.umd.js&#34;&gt;&lt;/script&gt;\n",
-       "&lt;link rel=&#34;stylesheet&#34; href=&#34;https://unpkg.com/pytket-circuit-renderer@0.10/dist/pytket-circuit-renderer.css&#34;&gt;\n",
-       "&lt;/head&gt;\n",
-       "&lt;body&gt;\n",
-       "\n",
-       "\n",
-       "    &lt;div id=&#34;circuit-display-vue-container-263764c6-112b-478e-b136-309e5b359aea&#34; class=&#34;pytket-circuit-display-container&#34;&gt;\n",
-       "        &lt;div style=&#34;display: none&#34;&gt;\n",
-       "            &lt;div id=&#34;circuit-json-to-display&#34;&gt;{&#34;bits&#34;: [], &#34;commands&#34;: [{&#34;args&#34;: [[&#34;q&#34;, [0]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [1]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [2]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [3]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [4]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [5]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [6]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}], &#34;created_qubits&#34;: [], &#34;discarded_qubits&#34;: [], &#34;implicit_permutation&#34;: [[[&#34;q&#34;, [0]], [&#34;q&#34;, [0]]], [[&#34;q&#34;, [1]], [&#34;q&#34;, [1]]], [[&#34;q&#34;, [2]], [&#34;q&#34;, [2]]], [[&#34;q&#34;, [3]], [&#34;q&#34;, [3]]], [[&#34;q&#34;, [4]], [&#34;q&#34;, [4]]], [[&#34;q&#34;, [5]], [&#34;q&#34;, [5]]], [[&#34;q&#34;, [6]], [&#34;q&#34;, [6]]]], &#34;phase&#34;: &#34;0.0&#34;, &#34;qubits&#34;: [[&#34;q&#34;, [0]], [&#34;q&#34;, [1]], [&#34;q&#34;, [2]], [&#34;q&#34;, [3]], [&#34;q&#34;, [4]], [&#34;q&#34;, [5]], [&#34;q&#34;, [6]]]}&lt;/div&gt;\n",
-       "        &lt;/div&gt;\n",
-       "        &lt;circuit-display-container\n",
-       "                :circuit-element-str=&#34;&#39;#circuit-json-to-display&#39;&#34;\n",
-       "                :init-render-options=&#34;initRenderOptions&#34;\n",
-       "                view-format=&#34;None&#34;\n",
-       "        &gt;&lt;/circuit-display-container&gt;\n",
-       "    &lt;/div&gt;\n",
-       "    &lt;script type=&#34;application/javascript&#34;&gt;\n",
-       "      const circuitRendererUid = &#34;263764c6-112b-478e-b136-309e5b359aea&#34;;\n",
-       "      const displayOptions = JSON.parse(&#39;{&#34;zxStyle&#34;: true, &#34;condenseCBits&#34;: false}&#39;);\n",
-       "\n",
-       "      // Script to initialise the circuit renderer app\n",
-       "\n",
-       "const { createApp } = Vue;\n",
-       "const circuitDisplayContainer = window[&#34;pytket-circuit-renderer&#34;].default;\n",
-       "// Init variables to be shared between circuit display instances\n",
-       "if (typeof window.pytketCircuitDisplays === &#34;undefined&#34;) {\n",
-       "    window.pytketCircuitDisplays = {};\n",
-       "}\n",
-       "// Create the root Vue component\n",
-       "const app = createApp({\n",
-       "    delimiters: [&#39;[[#&#39;, &#39;#]]&#39;],\n",
-       "    components: { circuitDisplayContainer },\n",
-       "    data () {\n",
-       "      return {\n",
-       "        initRenderOptions: displayOptions,\n",
-       "      }\n",
-       "    }\n",
-       "})\n",
-       "app.config.unwrapInjectedRef = true;\n",
-       "app.mount(&#34;#circuit-display-vue-container-&#34;+circuitRendererUid);\n",
-       "window.pytketCircuitDisplays[circuitRendererUid] = app;\n",
-       "    &lt;/script&gt;\n",
-       "\n",
-       "\n",
-       "\n",
-       "&lt;/body&gt;\n",
-       "&lt;/html&gt;\n",
-       "\"\n",
-       "            width=\"100%\" height=\"100%\"\n",
-       "            style=\"border: none; outline: none; overflow: auto\"></iframe>\n",
-       "</div>\n",
-       "\n"
-      ],
-      "text/plain": [
-       "<IPython.core.display.HTML object>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "from pytket import Circuit\n",
     "from pytket.circuit.display import render_circuit_jupyter as draw\n",
@@ -742,33 +641,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": null,
    "id": "aaea7e2f",
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
     }
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "new highest energy found:  2.8042\n",
-      "new highest energy found:  3.2636000000000003\n",
-      "new highest energy found:  3.570399999999999\n",
-      "new highest energy found:  3.6372000000000004\n",
-      "new highest energy found:  4.073799999999999\n",
-      "new highest energy found:  4.356799999999999\n",
-      "new highest energy found:  4.467\n",
-      "highest energy:  4.467\n",
-      "best guess mixer angles:  [0.597 0.742 0.064]\n",
-      "best guess cost angles:  [0.165 0.353 0.249]\n",
-      "CPU times: user 2min 15s, sys: 34.1 s, total: 2min 49s\n",
-      "Wall time: 42.3 s\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "%%time\n",
     "res = qaoa_calculate(backend, backend.default_compilation_pass(2).apply, shots = 5000, iterations = 100, seed=12345)"
@@ -776,28 +656,10 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": null,
    "id": "3b86301e-7645-4553-be38-3ebf89eedd37",
    "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Success ratio 0.202 \n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "import matplotlib.pyplot as plt\n",
     "\n",
@@ -842,31 +704,10 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 19,
+   "execution_count": null,
    "id": "ffce2a97-902c-44d8-8d64-b25498752907",
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "G = nx.Graph()\n",
     "G.add_edges_from(max_cut_graph_edges)\n",

From 89131360daf178c900d0d03510c2ac8df0966854 Mon Sep 17 00:00:00 2001
From: CalMacCQ <93673602+CalMacCQ@users.noreply.github.com>
Date: Mon, 23 Dec 2024 18:53:37 +0000
Subject: [PATCH 05/17] black formatting

---
 .../pytket_qaoa_maxcut_example.ipynb          | 76 ++++++++++++-------
 1 file changed, 48 insertions(+), 28 deletions(-)

diff --git a/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb b/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb
index 985cf29d..a5b4e1fd 100644
--- a/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb
+++ b/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb
@@ -37,10 +37,11 @@
    "source": [
     "import networkx as nx\n",
     "import matplotlib.pyplot as plt\n",
+    "\n",
     "G = nx.Graph()\n",
     "G.add_edges_from([(0, 1), (1, 2), (2, 0)])\n",
     "plt.figure(figsize=(2, 2))\n",
-    "nx.draw(G, node_color=['red', 'blue', 'red'])\n",
+    "nx.draw(G, node_color=[\"red\", \"blue\", \"red\"])\n",
     "plt.show()"
    ]
   },
@@ -211,6 +212,7 @@
    "outputs": [],
    "source": [
     "import warnings\n",
+    "\n",
     "warnings.filterwarnings(\"ignore\")"
    ]
   },
@@ -239,14 +241,14 @@
    "source": [
     "import networkx as nx\n",
     "\n",
-    "max_cut_graph_edges = [(0,1), (1,2), (1,3), (3,4), (4,5), (4,6)]\n",
+    "max_cut_graph_edges = [(0, 1), (1, 2), (1, 3), (3, 4), (4, 5), (4, 6)]\n",
     "n_nodes = 7\n",
     "\n",
     "max_cut_graph = nx.Graph()\n",
     "max_cut_graph.add_edges_from(max_cut_graph_edges)\n",
     "nx.draw(max_cut_graph, labels={node: node for node in max_cut_graph.nodes()})\n",
     "\n",
-    "expected_results = [(0,1,0,0,1,0,0), (1,0,1,1,0,1,1)]"
+    "expected_results = [(0, 1, 0, 0, 1, 0, 0), (1, 0, 1, 1, 0, 1, 1)]"
    ]
   },
   {
@@ -341,12 +343,14 @@
     "from pytket import Circuit\n",
     "from pytket.circuit.display import render_circuit_jupyter as draw\n",
     "\n",
+    "\n",
     "def qaoa_initial_circuit(n_qubits: int) -> Circuit:\n",
     "    c = Circuit(n_qubits)\n",
     "    for i in range(n_qubits):\n",
     "        c.H(i)\n",
     "    return c\n",
     "\n",
+    "\n",
     "superposition_circuit = qaoa_initial_circuit(n_nodes)\n",
     "\n",
     "draw(superposition_circuit)"
@@ -373,13 +377,14 @@
    "source": [
     "from pytket import Circuit\n",
     "\n",
+    "\n",
     "def build_cost_layer(graph: nx.Graph, gamma_val: float) -> Circuit:\n",
     "    circ = Circuit(graph.number_of_nodes())\n",
-    "    \n",
+    "\n",
     "    for i, j in list(graph.edges):\n",
     "        circ.ZZPhase(gamma_val, i, j)\n",
     "\n",
-    "    return circ\n"
+    "    return circ"
    ]
   },
   {
@@ -451,6 +456,7 @@
    "source": [
     "from pytket.backends.backendresult import BackendResult\n",
     "\n",
+    "\n",
     "def get_max_cut_energy(edges: list[tuple[int, int]], results: BackendResult) -> float:\n",
     "    energy = 0.0\n",
     "    dist = results.get_distribution()\n",
@@ -471,6 +477,7 @@
     "from typing import Callable\n",
     "import numpy as np\n",
     "\n",
+    "\n",
     "def qaoa_instance(\n",
     "    backend: Backend,\n",
     "    compiler_pass: Callable[[Circuit], bool],\n",
@@ -579,34 +586,31 @@
    },
    "outputs": [],
    "source": [
-    "def qaoa_calculate(backend: Backend,\n",
-    "                   compiler_pass: Callable[[Circuit], bool],\n",
-    "                   shots: int = 5000,\n",
-    "                   iterations: int = 100,\n",
-    "                   seed: int = 12345,\n",
-    "                  ) -> BackendResult:\n",
-    "    \n",
+    "def qaoa_calculate(\n",
+    "    backend: Backend,\n",
+    "    compiler_pass: Callable[[Circuit], bool],\n",
+    "    shots: int = 5000,\n",
+    "    iterations: int = 100,\n",
+    "    seed: int = 12345,\n",
+    ") -> BackendResult:\n",
+    "\n",
     "    # find the parameters for the highest energy\n",
-    "    best_mixer, best_cost = qaoa_optimise_energy(compiler_pass,\n",
-    "                                                 backend,\n",
-    "                                                 iterations,\n",
-    "                                                 3,\n",
-    "                                                 shots=shots,\n",
-    "                                                 seed=seed)\n",
-    "    \n",
+    "    best_mixer, best_cost = qaoa_optimise_energy(\n",
+    "        compiler_pass, backend, iterations, 3, shots=shots, seed=seed\n",
+    "    )\n",
+    "\n",
     "    # get the circuit with the final parameters of the optimisation:\n",
-    "    my_qaoa_circuit = qaoa_max_cut_circuit(max_cut_graph,\n",
-    "                                           n_nodes,\n",
-    "                                           best_mixer,\n",
-    "                                           best_cost)\n",
+    "    my_qaoa_circuit = qaoa_max_cut_circuit(\n",
+    "        max_cut_graph, n_nodes, best_mixer, best_cost\n",
+    "    )\n",
     "\n",
     "    my_qaoa_circuit.measure_all()\n",
     "\n",
     "    compiler_pass(my_qaoa_circuit)\n",
     "    handle = backend.process_circuit(my_qaoa_circuit, shots, seed=seed)\n",
     "\n",
-    "    result = backend.get_result(handle)    \n",
-    "    \n",
+    "    result = backend.get_result(handle)\n",
+    "\n",
     "    return result"
    ]
   },
@@ -651,7 +655,13 @@
    "outputs": [],
    "source": [
     "%%time\n",
-    "res = qaoa_calculate(backend, backend.default_compilation_pass(2).apply, shots = 5000, iterations = 100, seed=12345)"
+    "res = qaoa_calculate(\n",
+    "    backend,\n",
+    "    backend.default_compilation_pass(2).apply,\n",
+    "    shots=5000,\n",
+    "    iterations=100,\n",
+    "    seed=12345,\n",
+    ")"
    ]
   },
   {
@@ -663,6 +673,7 @@
    "source": [
     "import matplotlib.pyplot as plt\n",
     "\n",
+    "\n",
     "def plot_maxcut_results(result: BackendResult, n_strings: int) -> None:\n",
     "    \"\"\"\n",
     "    Plots Maxcut results in a barchart with the two most common bitstrings highlighted in green.\n",
@@ -691,6 +702,7 @@
     "    plt.ylabel(\"Number of Shots\")\n",
     "    plt.show()\n",
     "\n",
+    "\n",
     "plot_maxcut_results(res, 6)"
    ]
   },
@@ -716,9 +728,17 @@
     "H.add_edges_from(max_cut_graph_edges)\n",
     "\n",
     "plt.figure(1)\n",
-    "nx.draw(G, labels={node: node for node in max_cut_graph.nodes()}, node_color= ['red', 'blue', 'red','red', 'blue', 'red', 'red'])\n",
+    "nx.draw(\n",
+    "    G,\n",
+    "    labels={node: node for node in max_cut_graph.nodes()},\n",
+    "    node_color=[\"red\", \"blue\", \"red\", \"red\", \"blue\", \"red\", \"red\"],\n",
+    ")\n",
     "plt.figure(2)\n",
-    "nx.draw(H, labels={node: node for node in max_cut_graph.nodes()}, node_color= ['blue', 'red', 'blue', 'blue', 'red', 'blue', 'blue'])\n",
+    "nx.draw(\n",
+    "    H,\n",
+    "    labels={node: node for node in max_cut_graph.nodes()},\n",
+    "    node_color=[\"blue\", \"red\", \"blue\", \"blue\", \"red\", \"blue\", \"blue\"],\n",
+    ")\n",
     "\n",
     "plt.show()"
    ]

From a25550e079f75cc7d692ceebf5bcfe12519d8cc9 Mon Sep 17 00:00:00 2001
From: CalMacCQ <93673602+CalMacCQ@users.noreply.github.com>
Date: Mon, 23 Dec 2024 19:23:27 +0000
Subject: [PATCH 06/17] execute

---
 .../pytket_qaoa_maxcut_example.ipynb          | 199 ++++++++++++++++--
 1 file changed, 179 insertions(+), 20 deletions(-)

diff --git a/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb b/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb
index a5b4e1fd..eee2818d 100644
--- a/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb
+++ b/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb
@@ -26,14 +26,25 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 1,
    "id": "9456fbeb",
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
     }
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "image/png": "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",
+      "text/plain": [
+       "<Figure size 200x200 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "import networkx as nx\n",
     "import matplotlib.pyplot as plt\n",
@@ -230,14 +241,25 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 3,
    "id": "688f1332",
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
     }
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "import networkx as nx\n",
     "\n",
@@ -331,14 +353,93 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 4,
    "id": "0a9db628",
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
     }
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "\n",
+       "\n",
+       "\n",
+       "\n",
+       "\n",
+       "\n",
+       "<div style=\"resize: vertical; overflow: auto; height: 300px; display: block\">\n",
+       "    <iframe srcdoc=\"\n",
+       "&lt;!DOCTYPE html&gt;\n",
+       "&lt;html lang=&#34;en&#34;&gt;\n",
+       "&lt;head&gt;\n",
+       "    &lt;meta charset=&#34;UTF-8&#34;&gt;\n",
+       "    &lt;!-- Download Vue 3--&gt;\n",
+       "&lt;script type=&#34;application/javascript&#34; src=&#34;https://cdn.jsdelivr.net/npm/vue@3&#34;&gt;&lt;/script&gt;\n",
+       "&lt;!-- Download Circuit Renderer with styles --&gt;\n",
+       "&lt;script type=&#34;application/javascript&#34; src=&#34;https://unpkg.com/pytket-circuit-renderer@0.10/dist/pytket-circuit-renderer.umd.js&#34;&gt;&lt;/script&gt;\n",
+       "&lt;link rel=&#34;stylesheet&#34; href=&#34;https://unpkg.com/pytket-circuit-renderer@0.10/dist/pytket-circuit-renderer.css&#34;&gt;\n",
+       "&lt;/head&gt;\n",
+       "&lt;body&gt;\n",
+       "\n",
+       "\n",
+       "    &lt;div id=&#34;circuit-display-vue-container-505d2162-ae9b-48e3-a194-04b38e7ae8c5&#34; class=&#34;pytket-circuit-display-container&#34;&gt;\n",
+       "        &lt;div style=&#34;display: none&#34;&gt;\n",
+       "            &lt;div id=&#34;circuit-json-to-display&#34;&gt;{&#34;bits&#34;: [], &#34;commands&#34;: [{&#34;args&#34;: [[&#34;q&#34;, [0]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [1]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [2]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [3]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [4]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [5]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [6]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}], &#34;created_qubits&#34;: [], &#34;discarded_qubits&#34;: [], &#34;implicit_permutation&#34;: [[[&#34;q&#34;, [0]], [&#34;q&#34;, [0]]], [[&#34;q&#34;, [1]], [&#34;q&#34;, [1]]], [[&#34;q&#34;, [2]], [&#34;q&#34;, [2]]], [[&#34;q&#34;, [3]], [&#34;q&#34;, [3]]], [[&#34;q&#34;, [4]], [&#34;q&#34;, [4]]], [[&#34;q&#34;, [5]], [&#34;q&#34;, [5]]], [[&#34;q&#34;, [6]], [&#34;q&#34;, [6]]]], &#34;phase&#34;: &#34;0.0&#34;, &#34;qubits&#34;: [[&#34;q&#34;, [0]], [&#34;q&#34;, [1]], [&#34;q&#34;, [2]], [&#34;q&#34;, [3]], [&#34;q&#34;, [4]], [&#34;q&#34;, [5]], [&#34;q&#34;, [6]]]}&lt;/div&gt;\n",
+       "        &lt;/div&gt;\n",
+       "        &lt;circuit-display-container\n",
+       "                :circuit-element-str=&#34;&#39;#circuit-json-to-display&#39;&#34;\n",
+       "                :init-render-options=&#34;initRenderOptions&#34;\n",
+       "                view-format=&#34;None&#34;\n",
+       "        &gt;&lt;/circuit-display-container&gt;\n",
+       "    &lt;/div&gt;\n",
+       "    &lt;script type=&#34;application/javascript&#34;&gt;\n",
+       "      const circuitRendererUid = &#34;505d2162-ae9b-48e3-a194-04b38e7ae8c5&#34;;\n",
+       "      const displayOptions = JSON.parse(&#39;{&#34;zxStyle&#34;: true, &#34;condenseCBits&#34;: false}&#39;);\n",
+       "\n",
+       "      // Script to initialise the circuit renderer app\n",
+       "\n",
+       "const { createApp } = Vue;\n",
+       "const circuitDisplayContainer = window[&#34;pytket-circuit-renderer&#34;].default;\n",
+       "// Init variables to be shared between circuit display instances\n",
+       "if (typeof window.pytketCircuitDisplays === &#34;undefined&#34;) {\n",
+       "    window.pytketCircuitDisplays = {};\n",
+       "}\n",
+       "// Create the root Vue component\n",
+       "const app = createApp({\n",
+       "    delimiters: [&#39;[[#&#39;, &#39;#]]&#39;],\n",
+       "    components: { circuitDisplayContainer },\n",
+       "    data () {\n",
+       "      return {\n",
+       "        initRenderOptions: displayOptions,\n",
+       "      }\n",
+       "    }\n",
+       "})\n",
+       "app.config.unwrapInjectedRef = true;\n",
+       "app.mount(&#34;#circuit-display-vue-container-&#34;+circuitRendererUid);\n",
+       "window.pytketCircuitDisplays[circuitRendererUid] = app;\n",
+       "    &lt;/script&gt;\n",
+       "\n",
+       "\n",
+       "\n",
+       "&lt;/body&gt;\n",
+       "&lt;/html&gt;\n",
+       "\"\n",
+       "            width=\"100%\" height=\"100%\"\n",
+       "            style=\"border: none; outline: none; overflow: auto\"></iframe>\n",
+       "</div>\n",
+       "\n"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "from pytket import Circuit\n",
     "from pytket.circuit.display import render_circuit_jupyter as draw\n",
@@ -370,7 +471,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 5,
    "id": "57c9ed7e",
    "metadata": {},
    "outputs": [],
@@ -389,7 +490,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 6,
    "id": "5f43f97a",
    "metadata": {},
    "outputs": [],
@@ -413,7 +514,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 7,
    "id": "23f8910a",
    "metadata": {
     "slideshow": {
@@ -449,7 +550,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 8,
    "id": "df387eea-4198-428e-9b92-4f3bceb12f0e",
    "metadata": {},
    "outputs": [],
@@ -468,7 +569,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 9,
    "id": "e5abad7b-e989-4156-9708-3d8c97d8ca2a",
    "metadata": {},
    "outputs": [],
@@ -511,7 +612,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 10,
    "id": "0a44bed8",
    "metadata": {
     "slideshow": {
@@ -577,7 +678,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": 11,
    "id": "da46e63d",
    "metadata": {
     "slideshow": {
@@ -628,7 +729,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
+   "execution_count": 12,
    "id": "e7afb38e",
    "metadata": {
     "slideshow": {
@@ -645,14 +746,33 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 13,
    "id": "aaea7e2f",
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
     }
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "new highest energy found:  2.8042\n",
+      "new highest energy found:  3.2636000000000003\n",
+      "new highest energy found:  3.570399999999999\n",
+      "new highest energy found:  3.6372000000000004\n",
+      "new highest energy found:  4.073799999999999\n",
+      "new highest energy found:  4.356799999999999\n",
+      "new highest energy found:  4.467\n",
+      "highest energy:  4.467\n",
+      "best guess mixer angles:  [0.597 0.742 0.064]\n",
+      "best guess cost angles:  [0.165 0.353 0.249]\n",
+      "CPU times: user 2min 20s, sys: 34.1 s, total: 2min 55s\n",
+      "Wall time: 44.2 s\n"
+     ]
+    }
+   ],
    "source": [
     "%%time\n",
     "res = qaoa_calculate(\n",
@@ -666,10 +786,28 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 14,
    "id": "3b86301e-7645-4553-be38-3ebf89eedd37",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Success ratio 0.202 \n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "import matplotlib.pyplot as plt\n",
     "\n",
@@ -716,10 +854,31 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 15,
    "id": "ffce2a97-902c-44d8-8d64-b25498752907",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "G = nx.Graph()\n",
     "G.add_edges_from(max_cut_graph_edges)\n",

From 73839e3c6b5d2c39962c0e3b01440e0b118cdab6 Mon Sep 17 00:00:00 2001
From: CalMacCQ <93673602+CalMacCQ@users.noreply.github.com>
Date: Mon, 23 Dec 2024 20:06:38 +0000
Subject: [PATCH 07/17] factor of -2 improves results

---
 .../pytket_qaoa_maxcut_example.ipynb          | 40 +++++++++----------
 1 file changed, 19 insertions(+), 21 deletions(-)

diff --git a/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb b/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb
index eee2818d..b0227f53 100644
--- a/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb
+++ b/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb
@@ -36,7 +36,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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",
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",
       "text/plain": [
        "<Figure size 200x200 with 1 Axes>"
       ]
@@ -251,7 +251,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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",
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",
       "text/plain": [
        "<Figure size 640x480 with 1 Axes>"
       ]
@@ -385,7 +385,7 @@
        "&lt;body&gt;\n",
        "\n",
        "\n",
-       "    &lt;div id=&#34;circuit-display-vue-container-505d2162-ae9b-48e3-a194-04b38e7ae8c5&#34; class=&#34;pytket-circuit-display-container&#34;&gt;\n",
+       "    &lt;div id=&#34;circuit-display-vue-container-18cd89bd-852e-4c5c-a660-d1d8670d0fdf&#34; class=&#34;pytket-circuit-display-container&#34;&gt;\n",
        "        &lt;div style=&#34;display: none&#34;&gt;\n",
        "            &lt;div id=&#34;circuit-json-to-display&#34;&gt;{&#34;bits&#34;: [], &#34;commands&#34;: [{&#34;args&#34;: [[&#34;q&#34;, [0]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [1]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [2]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [3]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [4]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [5]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [6]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}], &#34;created_qubits&#34;: [], &#34;discarded_qubits&#34;: [], &#34;implicit_permutation&#34;: [[[&#34;q&#34;, [0]], [&#34;q&#34;, [0]]], [[&#34;q&#34;, [1]], [&#34;q&#34;, [1]]], [[&#34;q&#34;, [2]], [&#34;q&#34;, [2]]], [[&#34;q&#34;, [3]], [&#34;q&#34;, [3]]], [[&#34;q&#34;, [4]], [&#34;q&#34;, [4]]], [[&#34;q&#34;, [5]], [&#34;q&#34;, [5]]], [[&#34;q&#34;, [6]], [&#34;q&#34;, [6]]]], &#34;phase&#34;: &#34;0.0&#34;, &#34;qubits&#34;: [[&#34;q&#34;, [0]], [&#34;q&#34;, [1]], [&#34;q&#34;, [2]], [&#34;q&#34;, [3]], [&#34;q&#34;, [4]], [&#34;q&#34;, [5]], [&#34;q&#34;, [6]]]}&lt;/div&gt;\n",
        "        &lt;/div&gt;\n",
@@ -396,7 +396,7 @@
        "        &gt;&lt;/circuit-display-container&gt;\n",
        "    &lt;/div&gt;\n",
        "    &lt;script type=&#34;application/javascript&#34;&gt;\n",
-       "      const circuitRendererUid = &#34;505d2162-ae9b-48e3-a194-04b38e7ae8c5&#34;;\n",
+       "      const circuitRendererUid = &#34;18cd89bd-852e-4c5c-a660-d1d8670d0fdf&#34;;\n",
        "      const displayOptions = JSON.parse(&#39;{&#34;zxStyle&#34;: true, &#34;condenseCBits&#34;: false}&#39;);\n",
        "\n",
        "      // Script to initialise the circuit renderer app\n",
@@ -483,7 +483,7 @@
     "    circ = Circuit(graph.number_of_nodes())\n",
     "\n",
     "    for i, j in list(graph.edges):\n",
-    "        circ.ZZPhase(gamma_val, i, j)\n",
+    "        circ.ZZPhase(-gamma_val / 2, i, j)\n",
     "\n",
     "    return circ"
    ]
@@ -758,18 +758,16 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "new highest energy found:  2.8042\n",
-      "new highest energy found:  3.2636000000000003\n",
-      "new highest energy found:  3.570399999999999\n",
-      "new highest energy found:  3.6372000000000004\n",
-      "new highest energy found:  4.073799999999999\n",
-      "new highest energy found:  4.356799999999999\n",
-      "new highest energy found:  4.467\n",
-      "highest energy:  4.467\n",
-      "best guess mixer angles:  [0.597 0.742 0.064]\n",
-      "best guess cost angles:  [0.165 0.353 0.249]\n",
-      "CPU times: user 2min 20s, sys: 34.1 s, total: 2min 55s\n",
-      "Wall time: 44.2 s\n"
+      "new highest energy found:  3.1432\n",
+      "new highest energy found:  3.283599999999999\n",
+      "new highest energy found:  4.361\n",
+      "new highest energy found:  4.925600000000001\n",
+      "new highest energy found:  4.941999999999999\n",
+      "highest energy:  4.941999999999999\n",
+      "best guess mixer angles:  [0.392 0.247 0.138]\n",
+      "best guess cost angles:  [0.592 0.738 0.608]\n",
+      "CPU times: user 2min 21s, sys: 33.7 s, total: 2min 54s\n",
+      "Wall time: 42.1 s\n"
      ]
     }
    ],
@@ -794,12 +792,12 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Success ratio 0.202 \n"
+      "Success ratio 0.4252 \n"
      ]
     },
     {
      "data": {
-      "image/png": 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",
       "text/plain": [
        "<Figure size 640x480 with 1 Axes>"
       ]
@@ -860,7 +858,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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",
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",
       "text/plain": [
        "<Figure size 640x480 with 1 Axes>"
       ]
@@ -870,7 +868,7 @@
     },
     {
      "data": {
-      "image/png": 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",
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",
       "text/plain": [
        "<Figure size 640x480 with 1 Axes>"
       ]

From 2551bde8722f599714feddbf33f3ea8e702c3dc9 Mon Sep 17 00:00:00 2001
From: CalMacCQ <93673602+CalMacCQ@users.noreply.github.com>
Date: Mon, 23 Dec 2024 20:52:11 +0000
Subject: [PATCH 08/17] fix a sphinx warning

---
 .../pytket_qaoa_maxcut_example.ipynb           | 18 +++++++++---------
 1 file changed, 9 insertions(+), 9 deletions(-)

diff --git a/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb b/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb
index b0227f53..a4886809 100644
--- a/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb
+++ b/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb
@@ -36,7 +36,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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QFxfHxo0b+c9//qM6jigji8VCkyZN6N69u+ooujF04QD+9re/8c477/Duu+8a4imXr8jNzWXhwoVERUUZ6kmzYe/hitM0jf79+7N+/XpSU1O58cYbVUcS1xAfH8+QIUPYtWsXrVq1Uh1HNz5ROHAcPNO+fXtq167N+vXrCQgIUB1JXEW/fv349ddf2bJli+ooujLOWH0N1atXJz4+nu3btzN27FjVccRVnDx5kmXLlhliKddf+UzhAMLDw5k6dSrTpk0jLi5OdRxxBQsWLAAgIiJCcRL9+cyU8hJN04iMjGTp0qVs3brVUPcHRtGxY0caNGjAkiVLVEfRnc8VDiArK4uOHTtSsWJFNm/e7LXnYxjRrl27CA0NJSEhgYEDB6qOozufmlJeUrVqVRISEsjMzGTMmDGq44hiLBYL1apVo0+fPqqjuIRPFg7glltuYebMmcydO5e5c+eqjiNwLOWKiYkhIiLCsE+RfbZwACNGjOAf//gHo0ePZseOHarj+Lx169Zx8OBBQy3l+iufvIcrLicnhy5dunDhwgW2bt1KcHCw6kg+a9SoUaxdu5bMzEz8/PxUx3EJnx7hACpVqkR8fDzHjx/n8ccfl0OIFLlw4QIJCQkMHz7csGUDKRwALVq0YM6cOSxcuJDp06erjuOTvvnmG7Kysgz/AS0+P6Us7tlnn2XmzJn89NNPdOrUSXUcn3L//fdz7tw5NmzYoDqKS0nhisnPz+eOO+7g+PHjpKamUqNGDdWRfMLx48dp2LAh06ZN46mnnlIdx6VkSllMxYoVWbhwIVlZWYwYMQK73a46kk+YP38+ZrOZIUOGqI7iclK4v2jcuDHR0dEsXbqU9957T3Ucn2CxWOjTp49PzCikcKV44IEHeOmll5gwYQLr1q1THcfQfv75Z6xWqyF3BpRG7uGuoLCwkLvuuouMjAysVit169ZVHcmQxo0bx+zZszl69CgVK1ZUHcflZIS7An9/f+bPn4/dbicyMpKioiLVkQynqKiI2NhYIiIifKJsIIW7qvr16zN//nzWrFnDG2+8oTqO4fz4448cOXLEZ6aTIIW7pr///e9MnDiRSZMmsWLFCtVxDMVisdCiRQufes9T7uGug91up0+fPiQlJWG1WmnUqJHqSF4vOzubunXrMn78eJ86wlBGuOtgMpmwWCxUrlyZoUOHUlBQoDqS11u0aBHZ2dmGX8r1V1K461SzZk3i4uJISkpi/PjxquN4vejoaLp37+5zRxZK4cqgS5cuvPfee3zwwQcsWrRIdRyvdfToUX744QefelhyiRSujJ599lkGDhzIyJEj2bt3r+o4XmnevHlUqFCBQYMGqY7idvLQpBzOnTtHhw4dCA4OZuPGjQQGBqqO5FXatGlDaGioTx5VKCNcOYSEhJCQkIDNZuO5555THcerbN++nbS0NEMfo3A1Urhyatu2LR9//DGzZs0iNjZWdRyvER0dTe3atbn33ntVR1FCppRO0DSNESNG8NVXX5GcnExYWJjqSB6tsLCQRo0aMWTIED788EPVcZSQwjkpOzv78kqJpKQkgoKCFCfyXMuXL+e+++4jOTmZ8PBw1XGUkCmlk4KCgkhISODAgQM89dRTcgjRVVgsFkJDQ+nQoYPqKMpI4XQQGhrKp59+SkxMDJ999pnqOB4pKyuLRYsWGf5UrmuRwukkMjKSp556in/961+kpqaqjuNxvvrqK3Jzcxk2bJjqKErJPZyOcnNz6datG2fPniU1NZWQkBDVkTxGr1690DSN1atXq46ilIxwOgoMDCQ+Pp7Tp08zcuRIuZ+76NChQ/z4448+uZTrr6RwOmvWrBlffPEFixYt4n//+5/qOB4hNjaWwMBAQ378VFnJlNJFxo4dy4cffsjatWvp2rWr6jjKaJpG69atadu2LfPmzVMdRzkpnIsUFBTQs2dPDh48iNVqpVatWqojKZGSkkJ4eDjLli2jd+/equMoJ1NKF6lQoQJxcXHk5uYSFRXls4fKWiwW6taty1133aU6ikeQwrlQw4YNiY2NZeXKlbz99tuq47hdQUEB8+bNY9iwYfj7+6uO4xGkcC52zz338Morr/Daa6/53CPxlStXcvLkSZ/dGVAauYdzg6KiIu69917S0tLYtm0b9evXVx3JLSIiIti5cyfbt2/36dUlxckI5wZms5nY2FjMZjNDhw6lsLBQdSSXO3fuHEuWLPH5pVx/JYVzk7p16xIXF8eGDRt45ZVXVMdxuYSEBPLz84mMjFQdxaPIlNLNJk+ezLhx40hMTKRPnz6q47hMjx49CAgIYOXKlaqjeBQpnJvZ7XYefPBBNmzYgNVqpUmTJqoj6W7//v00bdqU6OhoeWDyFzKldDOTycSXX35JcHAwQ4YMIT8/X3Uk3cXExBAUFMRDDz2kOorHkcIpUKNGDeLj49m2bRtjx45VHUdXmqZhsVgYMGAAVapUUR3H40jhFOnYsSMffPABH3/8MfHx8arj6CYpKYmMjAzZGXAFcg+nkKZpDB06lGXLlrF161ZatmypOpLTxowZw6JFizh48CBms1l1HI8jhVMsKyuL8PBwAgMD2bx5M5UqVVIdqdzy8/Np0KABo0aNYvLkyarjeCSZUipWtWpVEhIS2LNnD2PGjFEdxynLli3j9OnTMp28CimcB7j11luZMWMGc+bM4YsvvlAdp9wsFgtt27bllltuUR3FY0nhPMSjjz7KyJEjGT16NGlpaarjlNmZM2dITEyU0e0a5B7Og1y4cIHOnTuTn59PcnIyVatWVR3pus2aNYvRo0dz5MgR6tWrpzqOx5LCeZiMjAzCw8O5//77mT9/vtcs/O3WrRvBwcEsW7ZMdRSPJlNKD9OyZUs+//xz4uLimDFjhuo412Xv3r1s3LhRppPXQQrngYYMGcKYMWN4/vnnSU5OVh3nmmJiYqhatSoPPvig6igeT6aUHiovL4/u3btz8uRJUlNTqV69uupIpdI0jRYtWnDHHXcwZ84c1XE8noxwHiogIID4+HjOnTvHiBEjPPYQok2bNrF3717ZFXCdpHAerEmTJkRHR5OYmMj777+vOk6poqOjadSoET169FAdxStI4Txcnz59GDduHC+//DLr169XHedP8vLyiIuLIyoqCpNJfpSuh9zDeYHCwkJ69epFZmYmVquVOnXqqI4EOD4RZ9CgQdhsNkJDQ1XH8QpSOC9x7Ngx2rZty6233sqKFSs8YiV+//79OXLkiFc8SfUUMg/wEvXr12f+/PmsXr2aiRMnqo7DqVOn+O677+RhSRlJ4bzInXfeyRtvvMGbb76p/HCeuLi4y/v5xPWTKaWXsdvt3H///aSkpGC1WmnYsKGSHJ07d6Z27dokJiYqeX1vJSOclzGZTMTExBAYGEhERAQFBQVuz7B79262bNkiS7nKQQrnhWrVqkVcXBxJSUm89NJLbn/9mJgYQkJC6Nu3r9tf29tJ4bxU165deffdd5kyZQpLlixx2+va7XYsFguDBw8mMDDQba9rFHIP58U0TWPgwIGsXr2a1NRUmjVr5vLXXLduHT169GDdunV0797d5a9nNFI4L3f27Fk6dOhAtWrV2LBhg8tHnccff5zvv/+evXv3yuqScpD/Yl6uWrVqxMfHk56ezvPPP+/S18rJyWHhwoUMHz5cylZO8l/NANq3b8+HH37IJ5984tIPrk9MTOT333+XN7udIFNKg9A0jeHDh7N48WKSk5NdsraxT58+nD59mk2bNul+bV8hhTOQ8+fP06lTJ/z8/EhKSiIoKEi3a584cYIGDRrw0UcfMXr0aN2u62tkSmkgVapUISEhgf379/P000+j5+/SBQsWYDKZiIiI0O2avkgKZzBhYWHMmjULi8XC7NmzdbtudHQ0DzzwADVr1tTtmr5ICmdAUVFRPPHEE4wZM4Zt27Y5fT2bzUZKSoo8LNGB3MMZVG5uLl27duX3338nJSWFkJCQcl/rpZdeYtasWRw7doyAgAAdU/oeGeEMKjAwkPj4eE6ePMmoUaPKfT9nt9uJiYkhIiJCyqYDKZyBNW/enLlz5/L111/z0Ucflesaa9as4fDhw7IzQCcypfQBL7zwAh9//DHr16+nc+fOpf8lTYOsLCgshMqV4eISsZEjR/LTTz+RkZHhNceuezIpnA8oKCigR48eHD58GKvV+seTxsOHYe5cWLMGtm6F33//44saN6YwPJwnv/2Wpi++yH/efFNJdqORwvmIQ4cO0a5dOzp16sTSmTMx/fvfsGgR+PmB3e4Y4f7CbjJhstspCg7GPH48jB0LFSooSG8cUjgfsnz5chbedx+fVKhARbsdioqu/4v9/KBNG4iNhdatXRfS4OShia/QNHpv2MAcwL+goGxlu/j1pKdD586webNLIvoCGeF8xZQpjimhs0wmx0OVpCSQw1/LTArnC7Zvhw4dyj6qXYnZ7JheJiWBv78+1/QRMqU0Orsd9F6SVVQE27bB1Kn6XtcHyAhndCtWQO/errl2rVpw5AhUrOia6xuQjHBGN22a66Z9p07B4sWuubZBSeGMrKDAMcIVFrrm+mYzfPuta65tUFI4I7PZHKVzlaIieYugjKRwRpae7vrXyMzU7+mnD5DCGVl2tutfw26HvDzXv45BSOGMzF3rHmV95XWTwhmZG44+p25dKVwZSOGMrF07x6JjVzGZ4PbbXXd9A5LCGVnVqo4lWK4sXY8erru2AUnhjO6ZZ0rd66YLsxlGjHDNtQ1KCmd0kZEQEqL/KGc2Q1QUyDmVZSKFM7qgIJg+Xd9Rzs8PgoPhv//V75o+QgrnCyIjoX9/x0MOPWgafPYZ1Kmjz/V8iBTOF/j5QUyMY7e2HqWbMgUGDnT+Oj5ICucrgoJg1SrHSAdlv6fz94eAAMfI9sILusfzFVI4X1K5MiQkwIIFUL26499da8S7tLWnUydIS4PHHnNtRoOTDai+KicH4uJgxgxISXGsifyroCDo1w/GjIEuXVz7fp6PkMIJR/l27ID9+x3beYKC4JZboHlz/R60CEAKJ4Rbya8vIdxICieEG0nhhHAjKZwQbiSFE8KNpHBCuJEUTgg3ksIJ4UZSOCHcSAonhBtJ4YRwIymcEG4khRPCjf4fsiB9nMKH4+QAAAAASUVORK5CYII=",
+      "image/png": "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",
       "text/plain": [
        "<Figure size 200x200 with 1 Axes>"
       ]
@@ -152,7 +152,7 @@
    "id": "de6b9e03",
    "metadata": {},
    "source": [
-    "## Cost function for Maxcut\n",
+    "## The cost function for Maxcut\n",
     "\n",
     "A solution to maxcut can be found by maximising the following cost function $C$ .\n",
     "\n",
@@ -251,7 +251,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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",
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",
       "text/plain": [
        "<Figure size 640x480 with 1 Axes>"
       ]
@@ -385,7 +385,7 @@
        "&lt;body&gt;\n",
        "\n",
        "\n",
-       "    &lt;div id=&#34;circuit-display-vue-container-18cd89bd-852e-4c5c-a660-d1d8670d0fdf&#34; class=&#34;pytket-circuit-display-container&#34;&gt;\n",
+       "    &lt;div id=&#34;circuit-display-vue-container-320fe13d-ad78-4d3d-bea3-6a3c1b353cca&#34; class=&#34;pytket-circuit-display-container&#34;&gt;\n",
        "        &lt;div style=&#34;display: none&#34;&gt;\n",
        "            &lt;div id=&#34;circuit-json-to-display&#34;&gt;{&#34;bits&#34;: [], &#34;commands&#34;: [{&#34;args&#34;: [[&#34;q&#34;, [0]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [1]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [2]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [3]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [4]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [5]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [6]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}], &#34;created_qubits&#34;: [], &#34;discarded_qubits&#34;: [], &#34;implicit_permutation&#34;: [[[&#34;q&#34;, [0]], [&#34;q&#34;, [0]]], [[&#34;q&#34;, [1]], [&#34;q&#34;, [1]]], [[&#34;q&#34;, [2]], [&#34;q&#34;, [2]]], [[&#34;q&#34;, [3]], [&#34;q&#34;, [3]]], [[&#34;q&#34;, [4]], [&#34;q&#34;, [4]]], [[&#34;q&#34;, [5]], [&#34;q&#34;, [5]]], [[&#34;q&#34;, [6]], [&#34;q&#34;, [6]]]], &#34;phase&#34;: &#34;0.0&#34;, &#34;qubits&#34;: [[&#34;q&#34;, [0]], [&#34;q&#34;, [1]], [&#34;q&#34;, [2]], [&#34;q&#34;, [3]], [&#34;q&#34;, [4]], [&#34;q&#34;, [5]], [&#34;q&#34;, [6]]]}&lt;/div&gt;\n",
        "        &lt;/div&gt;\n",
@@ -396,7 +396,7 @@
        "        &gt;&lt;/circuit-display-container&gt;\n",
        "    &lt;/div&gt;\n",
        "    &lt;script type=&#34;application/javascript&#34;&gt;\n",
-       "      const circuitRendererUid = &#34;18cd89bd-852e-4c5c-a660-d1d8670d0fdf&#34;;\n",
+       "      const circuitRendererUid = &#34;320fe13d-ad78-4d3d-bea3-6a3c1b353cca&#34;;\n",
        "      const displayOptions = JSON.parse(&#39;{&#34;zxStyle&#34;: true, &#34;condenseCBits&#34;: false}&#39;);\n",
        "\n",
        "      // Script to initialise the circuit renderer app\n",
@@ -766,8 +766,8 @@
       "highest energy:  4.941999999999999\n",
       "best guess mixer angles:  [0.392 0.247 0.138]\n",
       "best guess cost angles:  [0.592 0.738 0.608]\n",
-      "CPU times: user 2min 21s, sys: 33.7 s, total: 2min 54s\n",
-      "Wall time: 42.1 s\n"
+      "CPU times: user 2min 17s, sys: 33.8 s, total: 2min 51s\n",
+      "Wall time: 43.2 s\n"
      ]
     }
    ],
@@ -858,7 +858,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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3MGxY8OdUZx3Xnte/P1RWOkU3B9V2R7t1OzDPxLZqdUA+RpKkAy73AyUEzz6+9BI89hgce2xwrFGjYCh7d5HIf/fJ69YN5swJVqXu3v3A1qsD6phj9v5WaGjNm0OXLvv3MyRJCktuD3nvLhKBiRPhwgthyZIgYC5fDn/4A2zfHjwj2bMnnHBCMER+yimuRJ0nmjcPQuUf/7j/PqNv32BelyRJuSh/AmWtSCSYqDOoXpstKseddx5861up7OH9I4Ld3/+168+/Av656/dXAm32uiISgXPPbZg6JUnKRLm7bJBUDx99BJ07pxIouwDxttT52673P6tpU/j4Y2d4S5JyV348Qykl0akTXHJJKsPSfyfYS6muX132OrugIMaMGYZJSVJuM1BKu9x5Jxx8cENO0KkmEvk/Ro5c0lA3lCQpIxkopV3atIGnngq6lOnOxyoogKZNC+nV65ucccZQ7rrrLny6RJKUqwyU0m5OPhmeeSbYaGlfZ2X/dy38CMuXz2HmzJl89atfZcyYMWzYsKFB65UkKRM4KUeqQ0UFTJgA770H9fkbEolAnz7w5JPQq9d/jz/99NNMmjSJQw45hPLyco4//vgGr1mSpLDYoZTqUFoKK1cGSwm1bx8caxRnka3a4x06BM9hLl/+2TAJ8OUvf5mKigqKiooYNGgQjzzyyH6rXZKkA80OpZTEjh3wi1/Ayy/D0qXw/vvBsaZN4eijYeBAOO00GDUqfuistW3bNmbOnMn/+3//j0mTJnHffffRokWLA/OFSJK0nxgopRA89thjXH755Rx11FEsWLCAHj16hF2SJEn7zCFvKQQXXXQRS5cuZceOHfTv35/y8vKwS5IkaZ8ZKKWQ9O7dm7feeouRI0dy/vnnM3PmTHbs2BF2WZIk1ZtD3lLIYrEY999/P7NmzaK0tJSysjI6d+4cdlmSJKXMDqUUskgkwvTp01m0aBEff/wxffv25fnnnw+7LEmSUmaglDLECSecQEVFBSeeeCIjR47kpptuIhqNhl2WJElJOeQtZZiamhq++93vcuONNzJs2DDmzp1LSUlJ2GVJkhSXgVLKUK+88grjx4+noKCAp556iqFDh4ZdkiRJdXLIW8pQw4cPp7Kyku7duzN8+HDuuOMO/PlPkpSJDJRSBuvYsSMvv/wy1157LbNnz+bss89m3bp1YZclSdJnOOQtZYlnn32WiRMn0q5dO8rLy+nXr1/YJUmSBNihlLLGqFGjqKiooLi4mMGDBzNnzhyHwCVJGcFAKWWRI488ksWLFzNlyhSuuOIKJk6cyObNm8MuS5KU5xzylrLUvHnzmDp1Kp07d+ZnP/sZPXv2DLskSVKeskMpZanx48fz1ltvEYlEGDBgAHPnzg27JElSnjJQSlmsZ8+eLFu2jLPPPpsJEyYwbdo0qqqqwi5LkpRnHPKWckAsFuPBBx/kqquuonfv3pSXl3PkkUeGXZYkKU/YoZRyQCQS4bLLLuPNN99k7dq1lJaW8qtf/SrssiRJecJAKeWQ0tJSVqxYwcknn8yXvvQlrrvuOqqrq8MuS5KU4xzylnJQLBbje9/7Htdffz0nnXQS8+fPp2PHjmGXJUnKUQZKKYe9/vrrjB07lpqaGubNm8fw4cPDLkmSlIMc8pZy2NChQ6msrKRXr16MGDGC2267jZqamrDLkiTlGAOllONKSkp46aWXuOGGG7jhhhsYPXo0a9asCbssSVIOcchbyiMvvPACF154IS1btqS8vJwTTjgh7JIkSTnADqWUR84880wqKys59NBDGTJkCD/60Y/wZ0pJUroMlFKeOfzww3nttdeYNm0aV155JePGjWPTpk1hlyVJymIOeUt5rLy8nEsuuYSOHTuyYMECevfuHXZJkqQsZIdSymPnnXcey5cvp2nTpgwcOJCf/vSnYZckScpCBkopz/Xo0YMlS5Ywbtw4Jk2axNSpU9m2bVvYZUmSsohD3pI+9cgjjzB9+nSOOeYYFixYQLdu3cIuSZKUBexQSvrU5MmTWbJkCZs3b6a0tJSf//znYZckScoCBkpJn/G5z32O5cuXc9ppp3Huuefyta99jZ07d4ZdliQpgznkLalOsViMe+65h2uuuYYTTjiBp556isMOOyzssiRJGchAKSmhN998k/PPP5/t27czd+5cTjvttLBLkiRlGIe8JSU0aNAgKisr6devH2eccQb/8z//QzQaDbssSVIGsUMpKSU1NTXceuut3HLLLYwYMYInn3ySgw8+OOyyJEkZwEApqV5+85vfcMEFF9CkSRPKysoYPHhw2CVJkkLmkLekehkxYgSVlZV06dKFU045hbvuugt/LpWk/GaglFRvnTp14pVXXuHqq6/mq1/9KmPGjGHDhg1hlyVJColD3pLS8swzzzBp0iQOOuggFixYwPHHHx92SZKkA8wOpaS0nH322axYsYLWrVtz4okn8vDDDzsELkl5xkApKW3dunXjjTfe4Ctf+QpTpkzh4osvZuvWrWGXJUk6QBzyltSgHn/8cS6//HK6detGeXk5Rx99dNglSZL2MzuUkhrUxIkTWbZsGTt27KB///6UlZWFXZIkaT8zUEpqcL169eKtt95i1KhRjB07lquuuoodO3aEXZYkaT9xyFvSfhOLxbj//vuZNWsWpaWllJWV0blz57DLkiQ1MDuUkvabSCTC9OnTWbx4MatWraJv3748//zzYZclSWpgBkpJ+92AAQOoqKhg0KBBjBw5khtvvJFoNBp2WZKkBuKQt6QDpqamhjvuuIMbbriBYcOGMXfuXEpKSsIuS5KUJgOlpAPu1VdfZdy4cRQUFDB//nxOPvnksEuSJKXBIW9JB9ywYcOorKykR48enHrqqdxxxx3U1NSEXZYkaR8ZKCWFomPHjvzmN7/h61//OrNnz+bss89m3bp1YZclSdoHDnlLCt2zzz7LRRddRJs2bViwYAH9+vULuyRJUj3YoZQUulGjRlFRUcFBBx3E4MGDmTNnDv6sK0nZw0ApKSN06dKFRYsWMXXqVK644gouvPBCNm/eHHZZkqQUOOQtKePMnz+fKVOm0LlzZxYsWMCxxx4bdkmSpATsUErKOOPGjeOtt94iEokwYMAA5s6dG3ZJkqQEDJSSMlLPnj1ZtmwZ5557LhMmTGDatGlUVVWFXZYkqQ4OeUvKaLFYjIceeogrr7yS4447jvLyco488siwy5Ik7cYOpaSMFolEmDp1Km+88QZr166ltLSUX/7yl2GXJUnajYFSUlYoLS2loqKCYcOGcdZZZzF79myqq6vDLkuShEPekrJMLBbjBz/4AbNnz+akk05i/vz5dOzYMeyyJCmvGSglZaVFixYxduxYqqurmTdvHqeeemrYJUlS3nLIW1JWGjJkCJWVlfTu3ZvTTjuNW2+9lZqamrDLkqS8ZKCUlLUOOeQQXnzxRW644QZuuukmRo0axZo1a8IuS5LyjkPeknLCiy++yIQJE2jZsiVlZWUMHDgw7JIkKW/YoZSUE8444wwqKys59NBDGTp0KPfeey/+vCxJB4aBUlLOOPzww3nttdeYPn06V111FWPHjmXjxo1hlyVJOc8hb0k5acGCBUyePJmOHTuyYMECevfuXb8bbNsGf/wjrF8PhYVw6KFw1FFQ4M/hkrQn/88oKSeNGTOGFStW0KxZMwYOHMhPf/rT5BetWgW33gq9ekFREfTvDyNGwPDhcPTR0KoVnHoqzJsHO3bs/y9CkrKEHUpJOW3btm3MmDGDRx55hEsuuYR7772X5s2bf/akLVvgG9+A+++HmprgVzyFhRCNQvv2cM89MH48RCL794uQpAxnoJSUFx599FGmTZvG0UcfzYIFCzjqqKOCN956C8aMgX/+M3GQ3FMkArEYfOlL8Nhj0KbN/ilckrKAgVJS3nj77bcZM2YM//73v3n00Uc55+CD4YwzguHraHTfblpYGAyRv/YatG3boPVKUrYwUErKKxs3buSSSy5h5YIF/KFxY5pEo0TS3WGnsBBOPDEIlYWFDVOoJGURJ+VIyiutW7embN48ftelCwU7d9YZJt8BzgO6Ai2Ag4CTgV/Fu2k0CosXw91376eqJSmzGSgl5Z3Iww/T8e9/p3Gc9z8ENgFfAe4Gbtp1/EvAg4lufP318I9/NFidkpQtHPKWlF9iMejRAz74IPh9iqJAP2A78Kd4JxUWwnXXwbe/nX6dkpRF7FBKyi+/+x385S/1CpMAhcDhwPpEJ0Wj8MADsHPnvtcnSVnIQCkpv7z8MjRqlNKpW4D/AB8AdwHPA59PdtHatcEOO5KURwyUkvLLsmUpLxH0NeBg4CjgGuDLwI9SuXDFin2tTpKyUmo/pktSrnjvvZSHu68GxgD/AsoInqNMuuFi48bw/vtpFChJ2ccOpaT8UlWV8qnHACOAi4Bngc3AaCBpHK3HZ0hSLjBQSsove+7jXQ9jgLeAP+/Hz5CkbGSglJRfevWCgn37X9+2Xa8bEp20cyccc8w+3V+SspWBUlJ+GTAAIpGEp3xSx7GdwGNAc+DYZJ/Rr98+lSZJ2cqFzSXll2XLYODAhKd8GdhIsN1iJ2AV8CTBgubfB76a6OKOHYPdctzTW1IesUMpKb8MGAB9+iQc9h5L8D/HB4ArgB8AhwG/IEmYLCiAGTMMk5Lyjh1KSfln7lyYMKFBbxkDIi1bwl//Cocc0qD3lqRMZ4dSUv4ZPx7OPDPlHXNSEQHeHD/eMCkpLxkoJeWfSAQeegjatGmQ4elYQQEVhx3G4Ice4tJLL2Xbtm3JL5KkHGKglJSfOnWC3/4WWrdOL1QWFBA5+WT6vvceDz30EI8//jiDBg3iz39OulqlJOUMA6Wk/NWnDyxdGrwmWUpoL7WTeqZOheefJ9KiBZdccglLly5l69at9O/fn7KysoavWZIykIFSUn7r3j1YSui226BVq+BYonBZ+9zlUUfBb34Dc+ZAs2afvt2nTx9WrFjBF7/4RcaOHcuMGTOocitGSTnOWd6SVGvrVpg/P/i1bBls2GNPnCOOgKFD4ZJL4JRTEgbPWCzGnDlzuPrqq+nduzdlZWV07dp1P38BkhQOA6Uk1SUWg3/9KwiVhYVQUgJt29b7NitWrOD8889nzZo1/OQnP+Hss89u8FIlKWwGSknaz9avX8/kyZN5+umnmTVrFrfffjtNmjQJuyxJajAGSkk6AGKxGHfffTfXXnst/fr1o6ysjM6dO4ddliQ1CCflSNIBEIlEuPrqq1m0aBEff/wxffv25bnnngu7LElqEAZKSTqABg4cSGVlJYMHD2bUqFFcd911VFdXh12WJKXFIW9JCkFNTQ3f+973+MY3vsHgwYOZN28enTp1CrssSdonBkpJCtGiRYsYN24cO3bs4IknnuD0008PuyRJqjeHvCUpREOGDKGyspK+ffty5plncvPNNxONRsMuS5LqxQ6lJGWAmpoabrvtNm655RZOOeUU5s6dS4cOHcIuS5JSYqCUpAzyyiuvMH78eCKRCHPnzmX48OFhlyRJSTnkLUkZZPjw4axcuZKePXsyYsQIbr31VmpqasIuS5ISMlBKUobp0KEDCxcu5IYbbuCmm25i5MiRrF69OuyyJCkuh7wlKYO99NJLTJgwgaZNmzJ//nyGDBkSdkmStBc7lJKUwU4//XRWrlzJkUceybBhw7jzzjsdApeUcQyUkpThOnXqxCuvvMI111zD17/+dc466yzWrl0bdlmS9CmHvCUpizz77LNcdNFFtGrVirKyMgYOHBh2SZJkh1KSssmoUaNYuXIlhx56KEOHDuXuu+/GvoCksBkoJSnLdO7cmddee40ZM2Zw9dVXM2bMGNavXx92WZLymEPekpTFnn76aS6++GLat29PeXk5paWlYZckKQ/ZoZSkLPblL3+ZiooK2rZty6BBg3jggQccApd0wBkoJSnLde3alcWLFzNlyhSmTZvGBRdcwKZNm8IuS1IecchbknLIU089xdSpU+nYsSPl5eX06dMn7JIk5QE7lJKUQ8aOHcvy5ctp1qwZAwcO5OGHH3YIXNJ+Z6CUpBzTo0cPlixZwoUXXsiUKVOYNGkSW7ZsCbssSTnMIW9JymFPPPEEl112GV26dKG8vJxjjz027JIk5SA7lJKUwy688ELeeustAAYMGMATTzwRckWScpGBUpJy3LHHHsuyZcsYM2YMEydOZOrUqWzbti3ssiTlEIe8JSlPxGIxHn30UaZPn06PHj0oLy+nR48eYZclKQfYoZSkPBGJRJg8eTJLly5l+/bt9OvXj6eeeirssiTlAAOlJOWZPn36sHz5ckaNGsW4ceOYPn06VVVVYZclKYs55C1JeSoWi/HjH/+YmTNn0rt3b8rKyujatWvYZUnKQnYoJSlPRSIRLr/8ct58803WrVtHaWkpTz/9dNhlScpCBkpJynOlpaVUVFTw+c9/nnPOOYdZs2axY8eOsMuSlEUc8pYkAcEQ+D333MO1115LaWkpZWVldO7cOeyyJGUBO5SSJCAYAp85cyaLFi1i1apV9O3bl+eeey7ssiRlAQOlJOkzTjjhBCoqKhg8eDCjRo3iuuuuo7q6OuyyJGUwh7wlSXWqqanh+9//Ptdffz2DBg1i/vz5dOrUKeyyJGUgA6UkKaHFixczduxYqqqqePLJJzn99NPDLklShnHIW5KU0EknnURlZSX9+vXjzDPP5OabbyYajYZdlqQMYodSkpSSmpoavvOd73DzzTdzyimnMHfuXDp06BB2WZIygIFSklQvr776KuPHjycWizFv3jyGDx8edkmSQuaQtySpXoYNG0ZlZSXHHnssI0aM4Nvf/jY1NTVhlyUpRAZKSVK9dejQgYULF3LjjTdy880384UvfIHVq1eHXZakkDjkLUlKy8KFC5kwYQJNmjRh/vz5DBkyJOySJB1gdiglSWk57bTTqKyspGvXrgwbNow77rjDIXApzxgoJUlp69SpE7/97W+59tprmT17NmeddRZr164NuyxJB4hD3pKkBvXcc89x0UUXUVRURFlZGQMHDgy7JEn7mR1KSVKD+uIXv0hlZSWHHnooQ4cO5Yc//CH2LqTcZqCUJDW4zp0789prr3HllVcya9Yszj33XNavXx92WZL2E4e8JUn71TPPPMOkSZNo37495eXllJaWhl2SpAZmh1KStF+dffbZVFRU0K5dOwYNGsQDDzzgELiUYwyUkqT9rmvXrixevJhLL72UadOmMX78eDZt2hR2WZIaiEPekqQDqqysjClTptCxY0fKy8vp06dP2CVJSpMdSknSAXX++eezYsUKmjdvzsCBA3n44YcdApeynIFSknTAde/enTfffJOJEycyZcoUvvKVr7Bly5awy5K0jxzyliSF6oknnuCyyy6jS5culJeXc+yxx4ZdkqR6skMpSQrVhRdeyPLly4lEIgwYMIDHH3887JIk1ZOBUpIUup49e7J06VLOO+88LrroIqZMmcK2bdvCLktSihzyliRllEcffZRp06bRo0cPysvL6dGjR9glSUrCDqUkKaNcfPHFLF26lO3bt9OvXz+eeuqpsEuSlISBUpKUcfr06cPy5csZPXo048aNY9q0aWzfvj3ssiTF4ZC3JCljxWIxHnzwQa666iqOO+44ysvL6dq1a9hlSdqDHUpJUsaKRCJcdtllvPnmm6xfv57S0lKefvrpsMuStAcDpSQp45WWllJRUcGIESM455xzmDVrFjt27Ai7LEm7OOQtScoasViMe++9l2uuuYbS0lKeeuopjjjiiLDLkvKeHUpJUtaIRCJcddVVLFq0iFWrVtG3b1+effbZsMuS8p6BUpKUdU444QQqKioYMmQIo0ePZvbs2ezcuTPssqS85ZC3JClrxWIxvv/973PdddcxaNAg5s+fT6dOncIuS8o7BkpJUtZbvHgxY8eOpaqqiieffJLTTz+93vfYsQM+/hh27oSiIigpgUhkPxQr5SCHvCVJWe+kk05i5cqV9O/fnzPPPJObbrqJaDSa9Lo//Qm+9jXo2xdatoQuXaB7d+jYEdq2hREj4J57YP36/f0VSNnNDqUkKWfU1NRw++23c9NNN3HKKacwd+5cOnTosNd5770H06fDyy9Do0ZQXV33/Wo7lE2bBud/85vQosV+/AKkLGWglCTlnFdffZXx48cTi8WYN28ew4cPByAWg7vvhtmzoaYmfpCsS0EBdO4M8+bBiSfup8KlLOWQtyQp5wwbNoyVK1fSq1cvRowYwbe+9S2i0RpmzYJZs4LnJesTJiEIoP/4B5xyCrz00v6pW8pWdiglSTkrGo3yrW99i29+85t07foTPvjgorTvWVAAjRvDokXQv38DFCnlAAOlJCnn3XvvUq66agANNTBXWAhdu8Lbb0OzZg1ySymrOeQtScpp0Sjcd99ACgvrswbQrUAEOC7uPT/4AG67rSEqlLKfHUpJUk577jkYNao+V/wTOJogUHYB/hD3zNatYdUqaN48nQqVNWIxWLIkWB5g+XJ4913Yvj34BjjuuOAZiDPOCNahyjMGSklSTvvCF2DhwqCrmJpxwGogCvyHRIES4NFHYdKkdCpUxqupgccfhzvvhHfeCZ55iMWC47UKCoJ1pqJR6NcvWEpgzJi8WR3fIW9JUs7auTNoJqUeJn8HLAB+mNLZhYXwwgv7VpuyxN/+BsOHBz81/PGPwbFo9LNhEoI/136jVVbC+efDl74UbL+UBwyUkqSc9c47QahMTRS4EpgC9E7timgwAqoctXQpHH88vPFG8OdUB3Vrw+bzz0OfPvCHxF3uXGCglCTlrHffrc/Zc4APgW/V6zM+/DBY11I55ve/h89/HrZsqf+ipbWiUVi3Lli89C9/adj6MkyjsAuQJGl/2bYt1TPXADcDNwEH1/tz7rrrfg4+uBmtWrWidevWtGrVaq/fN27cuN73VUi2bYNzzw0m3KT+vETdolHYuBHGjQva2Y1yM3rl5lclSRLBHtypuREoJhjyrr//+Z8b2LZtfcJzmjVr9mm4TBQ8d/99vPeaNm1KJE8me4TilluCZyf3fE4SeBUYHueyN4E6d+WsroaKCvj+94PJOjnIWd6SpJy1ZAkMGpTsrPeBYwgm4oze7fg4YB3wItCaIHDuraQkWDqourqazZs3s2nTJjZu3MimTZv2+n2i93b//ebNm0n0z3OjRo1SCp6phNUWLVoYTnf3n/9Ax45xh7lfJQiUVwED9njvTOCgRPdu1Sr4ZmnRogEKzSx2KCVJOetznwtWc6mj0bSbj4AagohwVR3vHwnMpK6Z3wUFMHBg8PtGjRrRtm1b2rZtm1bNADU1NWzZsqVeIXTTpk1s2LCBf/7zn3u9F00wbFtQUEBRUVG9u6R1nVdUVERhYWHaX3+oHn442TcMAEOBMfW996ZNMH8+TJ68L5VlNAOlJClnNW8eBL6lSxNlhOOAp+s4fiOwCbgb6FbnlbEYnHpqQ1T6WQUFBZ+GtHTFYjG2bdtW7y7ppk2b+OSTT/Z6b0eSGUgtW7bcp2H8us4L5bnTuXNTCpQQfHc0px5hqqAA5s3LyUDpkLckKac9+SRceOG+XDmMZAubN20aLDPYrt2+1ZaNqqqqPhM6Uw2odQ39b0sya2r3507TeeY05edOq6qgqCjhrO5XCYa8i4DNQCFBt/JOoH8q/wFbt4b163NuwXMDpSQpp1VVQefOwaNxKTaedhlGokBZWAhTpsCcOenXmK9qnztN95nT2l+JNG7cOGnw7L5lC9Mfeijhfd4AfgCMJHhe8o/A94Atu95LadPF//s/OPzwVM7MGgZKSVLO+9Wvgk1LGkpBAbRvD++9l1/dyUy2+3On9emS7v77XqtXU7Z6db0/+y9AH+BkIKWNk95+G3qntnh+tjBQSpLywuTJ8NOf1rdLWbdIJAipX/xi+vdSBvnd74JFyPfBeODnwFaCYfCE3nkHjj12nz4nU7lTjiQpL8yZA2eeGXQXG+Jehskc1LHjPl96OLCDYOg7qZKSff6cTGWglCTlhSZN4OmnYerU4M/1DZaNGkHLlsGqL5de2vD1KQN067bPa0T+FWhGMFknoU6dguclcoyBUpKUN5o0CbqLL74Y/LsOweSaRGp3yjv9dPjTn2Ds2P1bo0JUu7Bogp826nrC8vfAL4HTSRKsGjWCIUPSKjFT+QylJCkvRaPw61/DAw8Ej85tqWOssmNH+PKXYdo06NXrwNeoEMydCxMmxH37VIK1JwcDhxDM8n4QaEyw9WLPZPd/6SU47bQGKTWTGCglSXmvpgY++CDYvvndd//C1VdPYeHCuxkx4nNhl6YDraoqaF+vXRusXL+He4AnCWZ2bwQOBj4P3AIclei+BQVwxBHwl780zIO8GcZAKUnSbj766CMOO+wwnnvuOUaOHBl2OQrDE0/AxIkNf99f/xq+8IWGv28GyL2ILElSGg455BAAVq1aFXIlCs2ECTB6dPIHbFNVUAAXX5yzYRIMlJIkfUbjxo0pLi7m3//+d9ilKCyRCDz2GPTsmX6oLCiAE0+EH/2oYWrLUAZKSZL2UFJSYqDMd23bwmuvwYAB6e27/fnPB8sK7ONyRNnCQClJ0h4MlAKguBhefx2+851gyZ9Uu5WFhdCsGdx/P7zwAhQlXZ0y6xkoJUnag4FSn2rUCGbPhvffh699Ddq0CY5HItC48X9/1TroILjhhmDZgCuuyMkZ3XVxlrckSXu4+uqrWbhwIe+8807YpSjT7NgBb78Ny5cHIbOqKuhGHnMM9OsHxx332YCZJxqFXYAkSZnGDqXiatIE+vcPfulT+dGHlSSpHkpKSlizZg07d+4MuxQpKxgoJUnaQ0lJCQCffPJJyJVI2cFAKUnSHmoDpcPeUmoMlJIk7cFAKdWPgVKSpD3Ubr9ooJRSY6CUJGkPTZs2pV27dgZKKUUGSkmS6uDSQVLqDJSSJNWhpKSEVatWhV2GlBUMlJIk1cEOpZQ6A6UkSXUwUEqpM1BKklQHA6WUOgOlJEl1qN1+sbq6OuxSpIxnoJQkqQ4dOnQgFouxevXqsEuRMp6BUpKkOrhbjpQ6A6UkSXWoDZQuHSQlZ6CUJKkObr8opc5AKUlSHZo1a0abNm0MlFIKDJSSJMXh0kFSagyUkiTFYaCUUmOglCQpDgOllBoDpSRJcXTo0MFAKaXAQClJUhx2KKXUGCglSYqjpKSE1atXu/2ilISBUpKkOEpKSojFYvznP/8JuxQpoxkoJUmKw+0XpdQYKCVJisNAKaXGQClJUhwGSik1BkpJkuJo3rw5rVu3NlBKSRgoJUlKwKWDpOQMlJIkJVBSUsKqVavCLkPKaAZKSZISsEMpJWeglCQpAQOllJyBUpKkBAyUUnIGSkmSEqjdfjEajYZdipSxDJSSJCXQoUMHampqWLNmTdilSBnLQClJUgIubi4lZ6CUJCmB2kDp0kFSfAZKSZISsEMpJWeglCQpgRYtWlBUVGSglBIwUEqSlIRLB0mJGSglSUrCQCklZqCUJCkJA6WUmIFSkqQkOnToYKCUEjBQSpKURElJicsGSQkYKCVJSqJ2+8WampqwS5EykoFSkqQkSkpKiEajbr8oxWGglCQpCRc3lxIzUEqSlISBUkrMQClJUhIGSikxA6UkSUkUFRXRsmVLA6UUh4FSkqQUuLi5FJ+BUpKkFLgWpRSfgVKSpBTYoZTiM1BKkpQCA6UUn4FSkqQUGCil+AyUkiSloKSkhE8++cTtF6U6GCglSUpBhw4dqK6uZt26dWGXImUcA6UkSSlwcXMpPgOlJEkpqA2ULh0k7c1AKUlSCuxQSvEZKCVJSkFRURHNmzc3UEp1MFBKkpSCSCTi0kFSHAZKSZJSZKCU6maglCQpRR06dDBQSnUwUEqSlCI7lFLdDJSSJKWopKTEZYOkOhgoJUlKUe32i7FYLOxSpIxioJQkKUUlJSXs3LnT7RelPRgoJUlKkYubS3VrFHYBkiRlhZoaDtu6lXMAHnsMeveGzp3h+OOhqCjk4qRwRWI+CCJJUt1iMViyBO67D555BrZs2fucSAT69IErroAJEwyXyksGSkmS6vLBB3DxxfD669CoEVRXxz83Eglei4rg7rth0qT/HpPygIFSkqQ9/fSncPnlQYhMFCT3FIkEXc2RI2HePGjdev/VKGUQA6UkSbu77z6YMSO9exQWwuc+B6+8YqhUXjBQSpJU69lnYfTohrlXYSGceiq8+KLD38p5LhskSRLA2rXBM5MFif9prAC+BBQDLYDjgHvqOjEahYUL4aGHGrpSKePYoZQkCYJh7jlzgiAYx0vAaKAvMBYoAj4AaoA74l3UogX885/Qrl3D1itlEAOlJEkbNkCHDrB9e9xTNgI9gMHAAuoxxBeJwF13wcyZaZcpZSqHvCVJmjsXqqoSnwL8G7iV4B/PLQSdyZTcd1861UkZz0ApSdLvfpf02cnfAK2Bj4CjCYa7WwNXAPH7mgTLCL3/Pqxe3TC1ShnIQClJ0pIlCZ+dBHgfqAbOAs4AfgZMBuYAF6fyGStWpFejlMHcy1uSpP/7v6SnbAa2Apfz31nd5wA7gB8D3wS6x7s4EoG//S3tMqVMZYdSkpTfYjGoSf40ZPNdr+P3OH7Brtc3E10cicDOnfWvTcoSBkpJUn6LRKBp06SnHbrrtWSP44fsel2X6OKammD5IClHGSglSerZM+kp/Xa9frTH8X/tej042Q2OO65+NUlZxEApSdLAgdAo8bSC83e9PrzH8YcIJiQMS3RxQUGwt7eUowyUkiSNGgXV1QlP6Uswq3suwS459xOEzHnAtfx3SHwvhYUwfDg0bx7vDCnruVOOJEnRKBxxBHy054D2Z+0EbgMeJRjqPgKYDlyd7P7PPANnnZV2mVKmMlBKkgRw//0wfXrD3rOwELp1g3feSTqkLmUzA6UkSRDMxB46FJYtSzr8nbKCgmDR9AEDGuZ+UobyGUpJkiAIf48/Dq1aBZ3FhvDNbxomlRcMlJIk1eraFV5+GVq3Tj9Ufv3r8I1vNExdUoYzUEqStLu+fWHpUujXL/m5e2rUKJjN/eMfw+23B4umS3nAQClJ0p66d4c33oAf/AAO3rVkebyOZSQSvBeJwOjR8O67cOmlhknlFSflSJKUyM6dwbI/v/hFMMHmr38N9v+GYGh8wAA4+WSYPBkOOyzUUqWwGCglSaqPHTtg69ZgeLtlSzuREgZKSZIkpclnKCVJkpQWA6UkSZLSYqCUJElSWgyUkiRJSouBUpIkSWkxUEqSJCktBkpJkiSlxUApSZKktBgoJUmSlBYDpSRJktJioJQkSVJaDJSSJElKi4FSkiRJaTFQSpIkKS0GSkmSJKXFQClJkqS0GCglSZKUFgOlJEmS0mKglCRJUloMlJIkSUqLgVKSJElpMVBKkiQpLQZKSZIkpcVAKUmSpLQYKCVJkpQWA6UkSZLSYqCUJElSWgyUkiRJSouBUpIkSWkxUEqSJCktBkpJkiSlxUApSZKktBgoJUmSlBYDpSRJktJioJQkSVJaDJSSJElKi4FSkiRJafn/eFdoCeW+UpYAAAAASUVORK5CYII=",
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",
       "text/plain": [
        "<Figure size 640x480 with 1 Axes>"
       ]
@@ -868,7 +868,7 @@
     },
     {
      "data": {
-      "image/png": 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",
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",
       "text/plain": [
        "<Figure size 640x480 with 1 Axes>"
       ]

From 21f112561ad9d4841fbed6c07e1dab9dba4dea3c Mon Sep 17 00:00:00 2001
From: CalMacCQ <93673602+CalMacCQ@users.noreply.github.com>
Date: Mon, 23 Dec 2024 21:43:21 +0000
Subject: [PATCH 09/17] lots of refactoring simplification

---
 .../pytket_qaoa_maxcut_example.ipynb          | 228 +++++++++++-------
 1 file changed, 139 insertions(+), 89 deletions(-)

diff --git a/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb b/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb
index a4886809..82208499 100644
--- a/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb
+++ b/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb
@@ -36,7 +36,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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+      "image/png": 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",
       "text/plain": [
        "<Figure size 200x200 with 1 Axes>"
       ]
@@ -251,7 +251,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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",
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",
       "text/plain": [
        "<Figure size 640x480 with 1 Axes>"
       ]
@@ -385,7 +385,7 @@
        "&lt;body&gt;\n",
        "\n",
        "\n",
-       "    &lt;div id=&#34;circuit-display-vue-container-320fe13d-ad78-4d3d-bea3-6a3c1b353cca&#34; class=&#34;pytket-circuit-display-container&#34;&gt;\n",
+       "    &lt;div id=&#34;circuit-display-vue-container-5be33b3b-9275-4cd7-8be6-3f860f6dd98b&#34; class=&#34;pytket-circuit-display-container&#34;&gt;\n",
        "        &lt;div style=&#34;display: none&#34;&gt;\n",
        "            &lt;div id=&#34;circuit-json-to-display&#34;&gt;{&#34;bits&#34;: [], &#34;commands&#34;: [{&#34;args&#34;: [[&#34;q&#34;, [0]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [1]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [2]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [3]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [4]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [5]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [6]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}], &#34;created_qubits&#34;: [], &#34;discarded_qubits&#34;: [], &#34;implicit_permutation&#34;: [[[&#34;q&#34;, [0]], [&#34;q&#34;, [0]]], [[&#34;q&#34;, [1]], [&#34;q&#34;, [1]]], [[&#34;q&#34;, [2]], [&#34;q&#34;, [2]]], [[&#34;q&#34;, [3]], [&#34;q&#34;, [3]]], [[&#34;q&#34;, [4]], [&#34;q&#34;, [4]]], [[&#34;q&#34;, [5]], [&#34;q&#34;, [5]]], [[&#34;q&#34;, [6]], [&#34;q&#34;, [6]]]], &#34;phase&#34;: &#34;0.0&#34;, &#34;qubits&#34;: [[&#34;q&#34;, [0]], [&#34;q&#34;, [1]], [&#34;q&#34;, [2]], [&#34;q&#34;, [3]], [&#34;q&#34;, [4]], [&#34;q&#34;, [5]], [&#34;q&#34;, [6]]]}&lt;/div&gt;\n",
        "        &lt;/div&gt;\n",
@@ -396,7 +396,7 @@
        "        &gt;&lt;/circuit-display-container&gt;\n",
        "    &lt;/div&gt;\n",
        "    &lt;script type=&#34;application/javascript&#34;&gt;\n",
-       "      const circuitRendererUid = &#34;320fe13d-ad78-4d3d-bea3-6a3c1b353cca&#34;;\n",
+       "      const circuitRendererUid = &#34;5be33b3b-9275-4cd7-8be6-3f860f6dd98b&#34;;\n",
        "      const displayOptions = JSON.parse(&#39;{&#34;zxStyle&#34;: true, &#34;condenseCBits&#34;: false}&#39;);\n",
        "\n",
        "      // Script to initialise the circuit renderer app\n",
@@ -529,17 +529,110 @@
     "\n",
     "    assert len(mixer_angles) == len(cost_angles)\n",
     "\n",
-    "    # Start from the uniform superposition state\n",
     "    qaoa_circuit = qaoa_initial_circuit(n_nodes)\n",
     "\n",
-    "    # add cost and mixer terms to state\n",
-    "    for cost, mixer in zip(cost_angles, mixer_angles):\n",
-    "        qaoa_circuit.append(build_cost_layer(graph, cost))\n",
-    "        qaoa_circuit.append(build_mixer_layer(n_nodes, mixer))\n",
+    "    # Iteratively append \"p\" cost and mixer layers\n",
+    "    for cost_angle, mixer_angle in zip(cost_angles, mixer_angles):\n",
+    "        qaoa_circuit.append(build_cost_layer(graph, cost_angle))\n",
+    "        qaoa_circuit.add_barrier(list(range(n_nodes)))\n",
+    "        qaoa_circuit.append(build_mixer_layer(n_nodes, mixer_angle))\n",
     "\n",
     "    return qaoa_circuit"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "id": "f97de321",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "\n",
+       "\n",
+       "\n",
+       "\n",
+       "\n",
+       "\n",
+       "<div style=\"resize: vertical; overflow: auto; height: 300px; display: block\">\n",
+       "    <iframe srcdoc=\"\n",
+       "&lt;!DOCTYPE html&gt;\n",
+       "&lt;html lang=&#34;en&#34;&gt;\n",
+       "&lt;head&gt;\n",
+       "    &lt;meta charset=&#34;UTF-8&#34;&gt;\n",
+       "    &lt;!-- Download Vue 3--&gt;\n",
+       "&lt;script type=&#34;application/javascript&#34; src=&#34;https://cdn.jsdelivr.net/npm/vue@3&#34;&gt;&lt;/script&gt;\n",
+       "&lt;!-- Download Circuit Renderer with styles --&gt;\n",
+       "&lt;script type=&#34;application/javascript&#34; src=&#34;https://unpkg.com/pytket-circuit-renderer@0.10/dist/pytket-circuit-renderer.umd.js&#34;&gt;&lt;/script&gt;\n",
+       "&lt;link rel=&#34;stylesheet&#34; href=&#34;https://unpkg.com/pytket-circuit-renderer@0.10/dist/pytket-circuit-renderer.css&#34;&gt;\n",
+       "&lt;/head&gt;\n",
+       "&lt;body&gt;\n",
+       "\n",
+       "\n",
+       "    &lt;div id=&#34;circuit-display-vue-container-8ea90544-6bf3-497d-9e5a-8a273ae135c3&#34; class=&#34;pytket-circuit-display-container&#34;&gt;\n",
+       "        &lt;div style=&#34;display: none&#34;&gt;\n",
+       "            &lt;div id=&#34;circuit-json-to-display&#34;&gt;{&#34;bits&#34;: [], &#34;commands&#34;: [{&#34;args&#34;: [[&#34;q&#34;, [0]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [1]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [2]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [0]], [&#34;q&#34;, [1]]], &#34;op&#34;: {&#34;params&#34;: [&#34;-0.375&#34;], &#34;type&#34;: &#34;ZZPhase&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [1]], [&#34;q&#34;, [2]]], &#34;op&#34;: {&#34;params&#34;: [&#34;-0.375&#34;], &#34;type&#34;: &#34;ZZPhase&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [0]], [&#34;q&#34;, [1]], [&#34;q&#34;, [2]]], &#34;op&#34;: {&#34;data&#34;: &#34;&#34;, &#34;signature&#34;: [&#34;Q&#34;, &#34;Q&#34;, &#34;Q&#34;], &#34;type&#34;: &#34;Barrier&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [0]]], &#34;op&#34;: {&#34;params&#34;: [&#34;0.8&#34;], &#34;type&#34;: &#34;Rx&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [1]]], &#34;op&#34;: {&#34;params&#34;: [&#34;0.8&#34;], &#34;type&#34;: &#34;Rx&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [2]]], &#34;op&#34;: {&#34;params&#34;: [&#34;0.8&#34;], &#34;type&#34;: &#34;Rx&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [0]], [&#34;q&#34;, [1]]], &#34;op&#34;: {&#34;params&#34;: [&#34;-0.3&#34;], &#34;type&#34;: &#34;ZZPhase&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [1]], [&#34;q&#34;, [2]]], &#34;op&#34;: {&#34;params&#34;: [&#34;-0.3&#34;], &#34;type&#34;: &#34;ZZPhase&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [0]], [&#34;q&#34;, [1]], [&#34;q&#34;, [2]]], &#34;op&#34;: {&#34;data&#34;: &#34;&#34;, &#34;signature&#34;: [&#34;Q&#34;, &#34;Q&#34;, &#34;Q&#34;], &#34;type&#34;: &#34;Barrier&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [0]]], &#34;op&#34;: {&#34;params&#34;: [&#34;0.1&#34;], &#34;type&#34;: &#34;Rx&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [1]]], &#34;op&#34;: {&#34;params&#34;: [&#34;0.1&#34;], &#34;type&#34;: &#34;Rx&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [2]]], &#34;op&#34;: {&#34;params&#34;: [&#34;0.1&#34;], &#34;type&#34;: &#34;Rx&#34;}}], &#34;created_qubits&#34;: [], &#34;discarded_qubits&#34;: [], &#34;implicit_permutation&#34;: [[[&#34;q&#34;, [0]], [&#34;q&#34;, [0]]], [[&#34;q&#34;, [1]], [&#34;q&#34;, [1]]], [[&#34;q&#34;, [2]], [&#34;q&#34;, [2]]]], &#34;phase&#34;: &#34;0.0&#34;, &#34;qubits&#34;: [[&#34;q&#34;, [0]], [&#34;q&#34;, [1]], [&#34;q&#34;, [2]]]}&lt;/div&gt;\n",
+       "        &lt;/div&gt;\n",
+       "        &lt;circuit-display-container\n",
+       "                :circuit-element-str=&#34;&#39;#circuit-json-to-display&#39;&#34;\n",
+       "                :init-render-options=&#34;initRenderOptions&#34;\n",
+       "                view-format=&#34;None&#34;\n",
+       "        &gt;&lt;/circuit-display-container&gt;\n",
+       "    &lt;/div&gt;\n",
+       "    &lt;script type=&#34;application/javascript&#34;&gt;\n",
+       "      const circuitRendererUid = &#34;8ea90544-6bf3-497d-9e5a-8a273ae135c3&#34;;\n",
+       "      const displayOptions = JSON.parse(&#39;{&#34;zxStyle&#34;: true, &#34;condenseCBits&#34;: false}&#39;);\n",
+       "\n",
+       "      // Script to initialise the circuit renderer app\n",
+       "\n",
+       "const { createApp } = Vue;\n",
+       "const circuitDisplayContainer = window[&#34;pytket-circuit-renderer&#34;].default;\n",
+       "// Init variables to be shared between circuit display instances\n",
+       "if (typeof window.pytketCircuitDisplays === &#34;undefined&#34;) {\n",
+       "    window.pytketCircuitDisplays = {};\n",
+       "}\n",
+       "// Create the root Vue component\n",
+       "const app = createApp({\n",
+       "    delimiters: [&#39;[[#&#39;, &#39;#]]&#39;],\n",
+       "    components: { circuitDisplayContainer },\n",
+       "    data () {\n",
+       "      return {\n",
+       "        initRenderOptions: displayOptions,\n",
+       "      }\n",
+       "    }\n",
+       "})\n",
+       "app.config.unwrapInjectedRef = true;\n",
+       "app.mount(&#34;#circuit-display-vue-container-&#34;+circuitRendererUid);\n",
+       "window.pytketCircuitDisplays[circuitRendererUid] = app;\n",
+       "    &lt;/script&gt;\n",
+       "\n",
+       "\n",
+       "\n",
+       "&lt;/body&gt;\n",
+       "&lt;/html&gt;\n",
+       "\"\n",
+       "            width=\"100%\" height=\"100%\"\n",
+       "            style=\"border: none; outline: none; overflow: auto\"></iframe>\n",
+       "</div>\n",
+       "\n"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "from networkx import path_graph\n",
+    "\n",
+    "three_vertex_path = path_graph(3)\n",
+    "\n",
+    "draw(qaoa_max_cut_circuit(three_vertex_path, 3, [0.8, 0.1], [0.75, 0.6]))"
+   ]
+  },
   {
    "cell_type": "markdown",
    "id": "bc2f8939-41b7-476b-a5a8-09de07211079",
@@ -550,7 +643,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 9,
    "id": "df387eea-4198-428e-9b92-4f3bceb12f0e",
    "metadata": {},
    "outputs": [],
@@ -558,7 +651,7 @@
     "from pytket.backends.backendresult import BackendResult\n",
     "\n",
     "\n",
-    "def get_max_cut_energy(edges: list[tuple[int, int]], results: BackendResult) -> float:\n",
+    "def energy_from_result(edges: list[tuple[int, int]], results: BackendResult) -> float:\n",
     "    energy = 0.0\n",
     "    dist = results.get_distribution()\n",
     "    for i, j in edges:\n",
@@ -569,7 +662,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 10,
    "id": "e5abad7b-e989-4156-9708-3d8c97d8ca2a",
    "metadata": {},
    "outputs": [],
@@ -579,23 +672,23 @@
     "import numpy as np\n",
     "\n",
     "\n",
-    "def qaoa_instance(\n",
+    "def eval_qaoa_energy(\n",
     "    backend: Backend,\n",
     "    compiler_pass: Callable[[Circuit], bool],\n",
     "    guess_mixer_angles: np.array,\n",
     "    guess_cost_angles: np.array,\n",
     "    seed: int,\n",
     "    shots: int = 5000,\n",
-    ") -> float:\n",
+    ") -> tuple[float, BackendResult]:\n",
     "    # step 1: get state guess\n",
     "    my_prep_circuit = qaoa_max_cut_circuit(\n",
     "        max_cut_graph, n_nodes, guess_mixer_angles, guess_cost_angles\n",
     "    )\n",
     "    measured_circ = my_prep_circuit.copy().measure_all()\n",
     "    compiler_pass(measured_circ)\n",
-    "    res = backend.run_circuit(measured_circ, shots, seed=seed)\n",
+    "    res: BackendResult = backend.run_circuit(measured_circ, shots, seed=seed)\n",
     "\n",
-    "    return get_max_cut_energy(max_cut_graph_edges, res)"
+    "    return energy_from_result(max_cut_graph_edges, res), res"
    ]
   },
   {
@@ -612,7 +705,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 11,
    "id": "0a44bed8",
    "metadata": {
     "slideshow": {
@@ -621,27 +714,28 @@
    },
    "outputs": [],
    "source": [
-    "def qaoa_optimise_energy(\n",
+    "def optimise_qaoa_energy(\n",
     "    compiler_pass: Callable[[Circuit], bool],\n",
     "    backend: Backend,\n",
     "    iterations: int = 100,\n",
     "    n: int = 3,\n",
     "    shots: int = 5000,\n",
     "    seed: int = 12345,\n",
-    "):\n",
+    ") -> tuple[BackendResult, np.array, np.array]:\n",
     "\n",
     "    highest_energy = 0\n",
     "    best_guess_mixer_angles = [0 for i in range(n)]\n",
     "    best_guess_cost_angles = [0 for i in range(n)]\n",
+    "    \n",
     "    rng = np.random.default_rng(seed)\n",
     "    # guess some angles (iterations)-times and try if they are better than the best angles found before\n",
     "\n",
-    "    for i in range(iterations):\n",
+    "    for _ in range(iterations):\n",
     "\n",
     "        guess_mixer_angles = rng.uniform(0, 1, n)\n",
     "        guess_cost_angles = rng.uniform(0, 1, n)\n",
     "\n",
-    "        qaoa_energy = qaoa_instance(\n",
+    "        qaoa_energy, result = eval_qaoa_energy(\n",
     "            backend,\n",
     "            compiler_pass,\n",
     "            guess_mixer_angles,\n",
@@ -657,11 +751,14 @@
     "            best_guess_mixer_angles = np.round(guess_mixer_angles, 3)\n",
     "            best_guess_cost_angles = np.round(guess_cost_angles, 3)\n",
     "            highest_energy = qaoa_energy\n",
+    "            best_result: BackendResult = result\n",
     "\n",
-    "    print(\"highest energy: \", highest_energy)\n",
-    "    print(\"best guess mixer angles: \", best_guess_mixer_angles)\n",
-    "    print(\"best guess cost angles: \", best_guess_cost_angles)\n",
-    "    return best_guess_mixer_angles, best_guess_cost_angles"
+    "    #print(\"highest energy: \", highest_energy)\n",
+    "    #print(\"best guess mixer angles: \", best_guess_mixer_angles)\n",
+    "    #print(\"best guess cost angles: \", best_guess_cost_angles)\n",
+    "    best_outputs = tuple([best_result, best_guess_cost_angles, best_guess_mixer_angles])\n",
+    "    print(best_outputs)\n",
+    "    return best_outputs"
    ]
   },
   {
@@ -676,57 +773,6 @@
     "## Calculate the State for the final Parameters"
    ]
   },
-  {
-   "cell_type": "code",
-   "execution_count": 11,
-   "id": "da46e63d",
-   "metadata": {
-    "slideshow": {
-     "slide_type": "fragment"
-    }
-   },
-   "outputs": [],
-   "source": [
-    "def qaoa_calculate(\n",
-    "    backend: Backend,\n",
-    "    compiler_pass: Callable[[Circuit], bool],\n",
-    "    shots: int = 5000,\n",
-    "    iterations: int = 100,\n",
-    "    seed: int = 12345,\n",
-    ") -> BackendResult:\n",
-    "\n",
-    "    # find the parameters for the highest energy\n",
-    "    best_mixer, best_cost = qaoa_optimise_energy(\n",
-    "        compiler_pass, backend, iterations, 3, shots=shots, seed=seed\n",
-    "    )\n",
-    "\n",
-    "    # get the circuit with the final parameters of the optimisation:\n",
-    "    my_qaoa_circuit = qaoa_max_cut_circuit(\n",
-    "        max_cut_graph, n_nodes, best_mixer, best_cost\n",
-    "    )\n",
-    "\n",
-    "    my_qaoa_circuit.measure_all()\n",
-    "\n",
-    "    compiler_pass(my_qaoa_circuit)\n",
-    "    handle = backend.process_circuit(my_qaoa_circuit, shots, seed=seed)\n",
-    "\n",
-    "    result = backend.get_result(handle)\n",
-    "\n",
-    "    return result"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "9dd97e10",
-   "metadata": {
-    "slideshow": {
-     "slide_type": "slide"
-    }
-   },
-   "source": [
-    "## Results with the Noiseless Simulator"
-   ]
-  },
   {
    "cell_type": "code",
    "execution_count": 12,
@@ -763,19 +809,23 @@
       "new highest energy found:  4.361\n",
       "new highest energy found:  4.925600000000001\n",
       "new highest energy found:  4.941999999999999\n",
-      "highest energy:  4.941999999999999\n",
-      "best guess mixer angles:  [0.392 0.247 0.138]\n",
-      "best guess cost angles:  [0.592 0.738 0.608]\n",
-      "CPU times: user 2min 17s, sys: 33.8 s, total: 2min 51s\n",
-      "Wall time: 43.2 s\n"
+      "(BackendResult(q_bits={},c_bits={c[0]: 0, c[1]: 1, c[2]: 2, c[3]: 3, c[4]: 4, c[5]: 5, c[6]: 6},counts=None,shots=[[182]\n",
+      " [ 72]\n",
+      " [ 72]\n",
+      " ...\n",
+      " [ 86]\n",
+      " [184]\n",
+      " [184]],state=None,unitary=None,density_matrix=None), array([0.592, 0.738, 0.608]), array([0.392, 0.247, 0.138]))\n",
+      "CPU times: user 2min 27s, sys: 33.4 s, total: 3min 1s\n",
+      "Wall time: 50.9 s\n"
      ]
     }
    ],
    "source": [
     "%%time\n",
-    "res = qaoa_calculate(\n",
-    "    backend,\n",
-    "    backend.default_compilation_pass(2).apply,\n",
+    "qaoa_result, cost_angles, mixer_angles = optimise_qaoa_energy(\n",
+    "    backend=backend,\n",
+    "    compiler_pass=backend.default_compilation_pass(2).apply,\n",
     "    shots=5000,\n",
     "    iterations=100,\n",
     "    seed=12345,\n",
@@ -792,12 +842,12 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Success ratio 0.4252 \n"
+      "Success ratio 0.4246 \n"
      ]
     },
     {
      "data": {
-      "image/png": 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",
       "text/plain": [
        "<Figure size 640x480 with 1 Axes>"
       ]
@@ -839,7 +889,7 @@
     "    plt.show()\n",
     "\n",
     "\n",
-    "plot_maxcut_results(res, 6)"
+    "plot_maxcut_results(qaoa_result, 6)"
    ]
   },
   {
@@ -858,7 +908,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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",
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",
       "text/plain": [
        "<Figure size 640x480 with 1 Axes>"
       ]
@@ -868,7 +918,7 @@
     },
     {
      "data": {
-      "image/png": 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",
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",
       "text/plain": [
        "<Figure size 640x480 with 1 Axes>"
       ]

From 7a59f9aa4cb210cc066d4008db54e67167ccb452 Mon Sep 17 00:00:00 2001
From: CalMacCQ <93673602+CalMacCQ@users.noreply.github.com>
Date: Mon, 23 Dec 2024 21:44:34 +0000
Subject: [PATCH 10/17] fix outputs

---
 .../pytket_qaoa_maxcut_example.ipynb          | 275 ++----------------
 1 file changed, 17 insertions(+), 258 deletions(-)

diff --git a/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb b/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb
index 82208499..213efea0 100644
--- a/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb
+++ b/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb
@@ -26,25 +26,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": null,
    "id": "9456fbeb",
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
     }
    },
-   "outputs": [
-    {
-     "data": {
-      "image/png": "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",
-      "text/plain": [
-       "<Figure size 200x200 with 1 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "import networkx as nx\n",
     "import matplotlib.pyplot as plt\n",
@@ -241,25 +230,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": null,
    "id": "688f1332",
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
     }
    },
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "import networkx as nx\n",
     "\n",
@@ -353,93 +331,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": null,
    "id": "0a9db628",
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
     }
    },
-   "outputs": [
-    {
-     "data": {
-      "text/html": [
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "<div style=\"resize: vertical; overflow: auto; height: 300px; display: block\">\n",
-       "    <iframe srcdoc=\"\n",
-       "&lt;!DOCTYPE html&gt;\n",
-       "&lt;html lang=&#34;en&#34;&gt;\n",
-       "&lt;head&gt;\n",
-       "    &lt;meta charset=&#34;UTF-8&#34;&gt;\n",
-       "    &lt;!-- Download Vue 3--&gt;\n",
-       "&lt;script type=&#34;application/javascript&#34; src=&#34;https://cdn.jsdelivr.net/npm/vue@3&#34;&gt;&lt;/script&gt;\n",
-       "&lt;!-- Download Circuit Renderer with styles --&gt;\n",
-       "&lt;script type=&#34;application/javascript&#34; src=&#34;https://unpkg.com/pytket-circuit-renderer@0.10/dist/pytket-circuit-renderer.umd.js&#34;&gt;&lt;/script&gt;\n",
-       "&lt;link rel=&#34;stylesheet&#34; href=&#34;https://unpkg.com/pytket-circuit-renderer@0.10/dist/pytket-circuit-renderer.css&#34;&gt;\n",
-       "&lt;/head&gt;\n",
-       "&lt;body&gt;\n",
-       "\n",
-       "\n",
-       "    &lt;div id=&#34;circuit-display-vue-container-5be33b3b-9275-4cd7-8be6-3f860f6dd98b&#34; class=&#34;pytket-circuit-display-container&#34;&gt;\n",
-       "        &lt;div style=&#34;display: none&#34;&gt;\n",
-       "            &lt;div id=&#34;circuit-json-to-display&#34;&gt;{&#34;bits&#34;: [], &#34;commands&#34;: [{&#34;args&#34;: [[&#34;q&#34;, [0]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [1]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [2]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [3]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [4]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [5]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [6]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}], &#34;created_qubits&#34;: [], &#34;discarded_qubits&#34;: [], &#34;implicit_permutation&#34;: [[[&#34;q&#34;, [0]], [&#34;q&#34;, [0]]], [[&#34;q&#34;, [1]], [&#34;q&#34;, [1]]], [[&#34;q&#34;, [2]], [&#34;q&#34;, [2]]], [[&#34;q&#34;, [3]], [&#34;q&#34;, [3]]], [[&#34;q&#34;, [4]], [&#34;q&#34;, [4]]], [[&#34;q&#34;, [5]], [&#34;q&#34;, [5]]], [[&#34;q&#34;, [6]], [&#34;q&#34;, [6]]]], &#34;phase&#34;: &#34;0.0&#34;, &#34;qubits&#34;: [[&#34;q&#34;, [0]], [&#34;q&#34;, [1]], [&#34;q&#34;, [2]], [&#34;q&#34;, [3]], [&#34;q&#34;, [4]], [&#34;q&#34;, [5]], [&#34;q&#34;, [6]]]}&lt;/div&gt;\n",
-       "        &lt;/div&gt;\n",
-       "        &lt;circuit-display-container\n",
-       "                :circuit-element-str=&#34;&#39;#circuit-json-to-display&#39;&#34;\n",
-       "                :init-render-options=&#34;initRenderOptions&#34;\n",
-       "                view-format=&#34;None&#34;\n",
-       "        &gt;&lt;/circuit-display-container&gt;\n",
-       "    &lt;/div&gt;\n",
-       "    &lt;script type=&#34;application/javascript&#34;&gt;\n",
-       "      const circuitRendererUid = &#34;5be33b3b-9275-4cd7-8be6-3f860f6dd98b&#34;;\n",
-       "      const displayOptions = JSON.parse(&#39;{&#34;zxStyle&#34;: true, &#34;condenseCBits&#34;: false}&#39;);\n",
-       "\n",
-       "      // Script to initialise the circuit renderer app\n",
-       "\n",
-       "const { createApp } = Vue;\n",
-       "const circuitDisplayContainer = window[&#34;pytket-circuit-renderer&#34;].default;\n",
-       "// Init variables to be shared between circuit display instances\n",
-       "if (typeof window.pytketCircuitDisplays === &#34;undefined&#34;) {\n",
-       "    window.pytketCircuitDisplays = {};\n",
-       "}\n",
-       "// Create the root Vue component\n",
-       "const app = createApp({\n",
-       "    delimiters: [&#39;[[#&#39;, &#39;#]]&#39;],\n",
-       "    components: { circuitDisplayContainer },\n",
-       "    data () {\n",
-       "      return {\n",
-       "        initRenderOptions: displayOptions,\n",
-       "      }\n",
-       "    }\n",
-       "})\n",
-       "app.config.unwrapInjectedRef = true;\n",
-       "app.mount(&#34;#circuit-display-vue-container-&#34;+circuitRendererUid);\n",
-       "window.pytketCircuitDisplays[circuitRendererUid] = app;\n",
-       "    &lt;/script&gt;\n",
-       "\n",
-       "\n",
-       "\n",
-       "&lt;/body&gt;\n",
-       "&lt;/html&gt;\n",
-       "\"\n",
-       "            width=\"100%\" height=\"100%\"\n",
-       "            style=\"border: none; outline: none; overflow: auto\"></iframe>\n",
-       "</div>\n",
-       "\n"
-      ],
-      "text/plain": [
-       "<IPython.core.display.HTML object>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "from pytket import Circuit\n",
     "from pytket.circuit.display import render_circuit_jupyter as draw\n",
@@ -542,89 +441,10 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": null,
    "id": "f97de321",
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/html": [
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "<div style=\"resize: vertical; overflow: auto; height: 300px; display: block\">\n",
-       "    <iframe srcdoc=\"\n",
-       "&lt;!DOCTYPE html&gt;\n",
-       "&lt;html lang=&#34;en&#34;&gt;\n",
-       "&lt;head&gt;\n",
-       "    &lt;meta charset=&#34;UTF-8&#34;&gt;\n",
-       "    &lt;!-- Download Vue 3--&gt;\n",
-       "&lt;script type=&#34;application/javascript&#34; src=&#34;https://cdn.jsdelivr.net/npm/vue@3&#34;&gt;&lt;/script&gt;\n",
-       "&lt;!-- Download Circuit Renderer with styles --&gt;\n",
-       "&lt;script type=&#34;application/javascript&#34; src=&#34;https://unpkg.com/pytket-circuit-renderer@0.10/dist/pytket-circuit-renderer.umd.js&#34;&gt;&lt;/script&gt;\n",
-       "&lt;link rel=&#34;stylesheet&#34; href=&#34;https://unpkg.com/pytket-circuit-renderer@0.10/dist/pytket-circuit-renderer.css&#34;&gt;\n",
-       "&lt;/head&gt;\n",
-       "&lt;body&gt;\n",
-       "\n",
-       "\n",
-       "    &lt;div id=&#34;circuit-display-vue-container-8ea90544-6bf3-497d-9e5a-8a273ae135c3&#34; class=&#34;pytket-circuit-display-container&#34;&gt;\n",
-       "        &lt;div style=&#34;display: none&#34;&gt;\n",
-       "            &lt;div id=&#34;circuit-json-to-display&#34;&gt;{&#34;bits&#34;: [], &#34;commands&#34;: [{&#34;args&#34;: [[&#34;q&#34;, [0]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [1]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [2]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [0]], [&#34;q&#34;, [1]]], &#34;op&#34;: {&#34;params&#34;: [&#34;-0.375&#34;], &#34;type&#34;: &#34;ZZPhase&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [1]], [&#34;q&#34;, [2]]], &#34;op&#34;: {&#34;params&#34;: [&#34;-0.375&#34;], &#34;type&#34;: &#34;ZZPhase&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [0]], [&#34;q&#34;, [1]], [&#34;q&#34;, [2]]], &#34;op&#34;: {&#34;data&#34;: &#34;&#34;, &#34;signature&#34;: [&#34;Q&#34;, &#34;Q&#34;, &#34;Q&#34;], &#34;type&#34;: &#34;Barrier&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [0]]], &#34;op&#34;: {&#34;params&#34;: [&#34;0.8&#34;], &#34;type&#34;: &#34;Rx&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [1]]], &#34;op&#34;: {&#34;params&#34;: [&#34;0.8&#34;], &#34;type&#34;: &#34;Rx&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [2]]], &#34;op&#34;: {&#34;params&#34;: [&#34;0.8&#34;], &#34;type&#34;: &#34;Rx&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [0]], [&#34;q&#34;, [1]]], &#34;op&#34;: {&#34;params&#34;: [&#34;-0.3&#34;], &#34;type&#34;: &#34;ZZPhase&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [1]], [&#34;q&#34;, [2]]], &#34;op&#34;: {&#34;params&#34;: [&#34;-0.3&#34;], &#34;type&#34;: &#34;ZZPhase&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [0]], [&#34;q&#34;, [1]], [&#34;q&#34;, [2]]], &#34;op&#34;: {&#34;data&#34;: &#34;&#34;, &#34;signature&#34;: [&#34;Q&#34;, &#34;Q&#34;, &#34;Q&#34;], &#34;type&#34;: &#34;Barrier&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [0]]], &#34;op&#34;: {&#34;params&#34;: [&#34;0.1&#34;], &#34;type&#34;: &#34;Rx&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [1]]], &#34;op&#34;: {&#34;params&#34;: [&#34;0.1&#34;], &#34;type&#34;: &#34;Rx&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [2]]], &#34;op&#34;: {&#34;params&#34;: [&#34;0.1&#34;], &#34;type&#34;: &#34;Rx&#34;}}], &#34;created_qubits&#34;: [], &#34;discarded_qubits&#34;: [], &#34;implicit_permutation&#34;: [[[&#34;q&#34;, [0]], [&#34;q&#34;, [0]]], [[&#34;q&#34;, [1]], [&#34;q&#34;, [1]]], [[&#34;q&#34;, [2]], [&#34;q&#34;, [2]]]], &#34;phase&#34;: &#34;0.0&#34;, &#34;qubits&#34;: [[&#34;q&#34;, [0]], [&#34;q&#34;, [1]], [&#34;q&#34;, [2]]]}&lt;/div&gt;\n",
-       "        &lt;/div&gt;\n",
-       "        &lt;circuit-display-container\n",
-       "                :circuit-element-str=&#34;&#39;#circuit-json-to-display&#39;&#34;\n",
-       "                :init-render-options=&#34;initRenderOptions&#34;\n",
-       "                view-format=&#34;None&#34;\n",
-       "        &gt;&lt;/circuit-display-container&gt;\n",
-       "    &lt;/div&gt;\n",
-       "    &lt;script type=&#34;application/javascript&#34;&gt;\n",
-       "      const circuitRendererUid = &#34;8ea90544-6bf3-497d-9e5a-8a273ae135c3&#34;;\n",
-       "      const displayOptions = JSON.parse(&#39;{&#34;zxStyle&#34;: true, &#34;condenseCBits&#34;: false}&#39;);\n",
-       "\n",
-       "      // Script to initialise the circuit renderer app\n",
-       "\n",
-       "const { createApp } = Vue;\n",
-       "const circuitDisplayContainer = window[&#34;pytket-circuit-renderer&#34;].default;\n",
-       "// Init variables to be shared between circuit display instances\n",
-       "if (typeof window.pytketCircuitDisplays === &#34;undefined&#34;) {\n",
-       "    window.pytketCircuitDisplays = {};\n",
-       "}\n",
-       "// Create the root Vue component\n",
-       "const app = createApp({\n",
-       "    delimiters: [&#39;[[#&#39;, &#39;#]]&#39;],\n",
-       "    components: { circuitDisplayContainer },\n",
-       "    data () {\n",
-       "      return {\n",
-       "        initRenderOptions: displayOptions,\n",
-       "      }\n",
-       "    }\n",
-       "})\n",
-       "app.config.unwrapInjectedRef = true;\n",
-       "app.mount(&#34;#circuit-display-vue-container-&#34;+circuitRendererUid);\n",
-       "window.pytketCircuitDisplays[circuitRendererUid] = app;\n",
-       "    &lt;/script&gt;\n",
-       "\n",
-       "\n",
-       "\n",
-       "&lt;/body&gt;\n",
-       "&lt;/html&gt;\n",
-       "\"\n",
-       "            width=\"100%\" height=\"100%\"\n",
-       "            style=\"border: none; outline: none; overflow: auto\"></iframe>\n",
-       "</div>\n",
-       "\n"
-      ],
-      "text/plain": [
-       "<IPython.core.display.HTML object>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "from networkx import path_graph\n",
     "\n",
@@ -753,11 +573,10 @@
     "            highest_energy = qaoa_energy\n",
     "            best_result: BackendResult = result\n",
     "\n",
-    "    #print(\"highest energy: \", highest_energy)\n",
-    "    #print(\"best guess mixer angles: \", best_guess_mixer_angles)\n",
-    "    #print(\"best guess cost angles: \", best_guess_cost_angles)\n",
+    "    print(\"highest energy: \", highest_energy)\n",
+    "    print(\"best guess mixer angles: \", best_guess_mixer_angles)\n",
+    "    print(\"best guess cost angles: \", best_guess_cost_angles)\n",
     "    best_outputs = tuple([best_result, best_guess_cost_angles, best_guess_mixer_angles])\n",
-    "    print(best_outputs)\n",
     "    return best_outputs"
    ]
   },
@@ -792,35 +611,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": null,
    "id": "aaea7e2f",
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
     }
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "new highest energy found:  3.1432\n",
-      "new highest energy found:  3.283599999999999\n",
-      "new highest energy found:  4.361\n",
-      "new highest energy found:  4.925600000000001\n",
-      "new highest energy found:  4.941999999999999\n",
-      "(BackendResult(q_bits={},c_bits={c[0]: 0, c[1]: 1, c[2]: 2, c[3]: 3, c[4]: 4, c[5]: 5, c[6]: 6},counts=None,shots=[[182]\n",
-      " [ 72]\n",
-      " [ 72]\n",
-      " ...\n",
-      " [ 86]\n",
-      " [184]\n",
-      " [184]],state=None,unitary=None,density_matrix=None), array([0.592, 0.738, 0.608]), array([0.392, 0.247, 0.138]))\n",
-      "CPU times: user 2min 27s, sys: 33.4 s, total: 3min 1s\n",
-      "Wall time: 50.9 s\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "%%time\n",
     "qaoa_result, cost_angles, mixer_angles = optimise_qaoa_energy(\n",
@@ -834,28 +632,10 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": null,
    "id": "3b86301e-7645-4553-be38-3ebf89eedd37",
    "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Success ratio 0.4246 \n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "import matplotlib.pyplot as plt\n",
     "\n",
@@ -902,31 +682,10 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": null,
    "id": "ffce2a97-902c-44d8-8d64-b25498752907",
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "G = nx.Graph()\n",
     "G.add_edges_from(max_cut_graph_edges)\n",

From 889bce61eccb845f9707d771e2297c840d22651e Mon Sep 17 00:00:00 2001
From: CalMacCQ <93673602+CalMacCQ@users.noreply.github.com>
Date: Mon, 23 Dec 2024 22:42:16 +0000
Subject: [PATCH 11/17] more refactoring cleanup

---
 .../pytket_qaoa_maxcut_example.ipynb          | 49 ++++++++++++-------
 1 file changed, 31 insertions(+), 18 deletions(-)

diff --git a/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb b/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb
index 213efea0..2a8c545f 100644
--- a/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb
+++ b/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb
@@ -286,7 +286,7 @@
    "source": [
     "$$\n",
     "\\begin{equation}\n",
-    "H_P = 3 I^{\\otimes 6} -0.5 \\big[ Z_0 Z_1 + Z_1 Z_2 +Z_1 Z_3 +Z_3 Z_4 +Z_4 Z_5 +Z_4 Z_6  \\big]\n",
+    "H_P = 3 I^{\\otimes 7} -0.5 \\big[ Z_0 Z_1 + Z_1 Z_2 +Z_1 Z_3 +Z_3 Z_4 +Z_4 Z_5 +Z_4 Z_6  \\big]\n",
     "\\end{equation}\n",
     "$$\n",
     "\n",
@@ -422,9 +422,11 @@
    },
    "outputs": [],
    "source": [
-    "def qaoa_max_cut_circuit(\n",
-    "    graph: nx.Graph, n_nodes: int, mixer_angles: list[float], cost_angles: list[float]\n",
+    "def build_qaoa_circuit(\n",
+    "    graph: nx.Graph, mixer_angles: list[float], cost_angles: list[float]\n",
     ") -> Circuit:\n",
+    "    \n",
+    "    n_nodes = graph.number_of_nodes()\n",
     "\n",
     "    assert len(mixer_angles) == len(cost_angles)\n",
     "\n",
@@ -436,6 +438,7 @@
     "        qaoa_circuit.add_barrier(list(range(n_nodes)))\n",
     "        qaoa_circuit.append(build_mixer_layer(n_nodes, mixer_angle))\n",
     "\n",
+    "    qaoa_circuit.measure_all()\n",
     "    return qaoa_circuit"
    ]
   },
@@ -450,7 +453,7 @@
     "\n",
     "three_vertex_path = path_graph(3)\n",
     "\n",
-    "draw(qaoa_max_cut_circuit(three_vertex_path, 3, [0.8, 0.1], [0.75, 0.6]))"
+    "draw(build_qaoa_circuit(three_vertex_path, [0.8, 0.1], [0.75, 0.6]))"
    ]
   },
   {
@@ -471,7 +474,8 @@
     "from pytket.backends.backendresult import BackendResult\n",
     "\n",
     "\n",
-    "def energy_from_result(edges: list[tuple[int, int]], results: BackendResult) -> float:\n",
+    "def energy_from_result(graph: nx.Graph, results: BackendResult) -> float:\n",
+    "    edges = list(graph.edges)\n",
     "    energy = 0.0\n",
     "    dist = results.get_distribution()\n",
     "    for i, j in edges:\n",
@@ -488,6 +492,7 @@
    "outputs": [],
    "source": [
     "from pytket.backends.backend import Backend\n",
+    "from pytket.passes import RemoveBarriers\n",
     "from typing import Callable\n",
     "import numpy as np\n",
     "\n",
@@ -497,18 +502,24 @@
     "    compiler_pass: Callable[[Circuit], bool],\n",
     "    guess_mixer_angles: np.array,\n",
     "    guess_cost_angles: np.array,\n",
+    "    graph: nx.Graph,\n",
     "    seed: int,\n",
     "    shots: int = 5000,\n",
     ") -> tuple[float, BackendResult]:\n",
-    "    # step 1: get state guess\n",
-    "    my_prep_circuit = qaoa_max_cut_circuit(\n",
-    "        max_cut_graph, n_nodes, guess_mixer_angles, guess_cost_angles\n",
+    "    \n",
+    "    # Build Circuit\n",
+    "    qaoa_circuit = build_qaoa_circuit(\n",
+    "        graph=graph, cost_angles=guess_cost_angles, mixer_angles=guess_mixer_angles\n",
     "    )\n",
-    "    measured_circ = my_prep_circuit.copy().measure_all()\n",
-    "    compiler_pass(measured_circ)\n",
-    "    res: BackendResult = backend.run_circuit(measured_circ, shots, seed=seed)\n",
     "\n",
-    "    return energy_from_result(max_cut_graph_edges, res), res"
+    "    # Compile\n",
+    "    RemoveBarriers().apply(qaoa_circuit)\n",
+    "    compiler_pass(qaoa_circuit)\n",
+    "\n",
+    "    # Execute\n",
+    "    result: BackendResult = backend.run_circuit(qaoa_circuit, shots, seed=seed)\n",
+    "\n",
+    "    return energy_from_result(graph, result), result"
    ]
   },
   {
@@ -535,25 +546,25 @@
    "outputs": [],
    "source": [
     "def optimise_qaoa_energy(\n",
+    "    graph: nx.Graph,\n",
     "    compiler_pass: Callable[[Circuit], bool],\n",
     "    backend: Backend,\n",
     "    iterations: int = 100,\n",
-    "    n: int = 3,\n",
+    "    p_value: int = 3,\n",
     "    shots: int = 5000,\n",
     "    seed: int = 12345,\n",
     ") -> tuple[BackendResult, np.array, np.array]:\n",
     "\n",
     "    highest_energy = 0\n",
-    "    best_guess_mixer_angles = [0 for i in range(n)]\n",
-    "    best_guess_cost_angles = [0 for i in range(n)]\n",
+    "    best_guess_mixer_angles = [0 for _ in range(p_value)]\n",
+    "    best_guess_cost_angles = [0 for _ in range(p_value)]\n",
     "    \n",
     "    rng = np.random.default_rng(seed)\n",
-    "    # guess some angles (iterations)-times and try if they are better than the best angles found before\n",
     "\n",
     "    for _ in range(iterations):\n",
     "\n",
-    "        guess_mixer_angles = rng.uniform(0, 1, n)\n",
-    "        guess_cost_angles = rng.uniform(0, 1, n)\n",
+    "        guess_mixer_angles = rng.uniform(0, 1, p_value)\n",
+    "        guess_cost_angles = rng.uniform(0, 1, p_value)\n",
     "\n",
     "        qaoa_energy, result = eval_qaoa_energy(\n",
     "            backend,\n",
@@ -562,6 +573,7 @@
     "            guess_cost_angles,\n",
     "            seed=seed,\n",
     "            shots=shots,\n",
+    "            graph=graph,\n",
     "        )\n",
     "\n",
     "        if qaoa_energy > highest_energy:\n",
@@ -626,6 +638,7 @@
     "    compiler_pass=backend.default_compilation_pass(2).apply,\n",
     "    shots=5000,\n",
     "    iterations=100,\n",
+    "    graph=max_cut_graph,\n",
     "    seed=12345,\n",
     ")"
    ]

From 07c19566d66edc170c31f9f24a3e6fb5c1261c49 Mon Sep 17 00:00:00 2001
From: CalMacCQ <93673602+CalMacCQ@users.noreply.github.com>
Date: Mon, 23 Dec 2024 22:54:57 +0000
Subject: [PATCH 12/17] more cleanup and formatting

---
 .../pytket_qaoa_maxcut_example.ipynb          | 21 +++++++++----------
 1 file changed, 10 insertions(+), 11 deletions(-)

diff --git a/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb b/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb
index 2a8c545f..445d5477 100644
--- a/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb
+++ b/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb
@@ -425,7 +425,7 @@
     "def build_qaoa_circuit(\n",
     "    graph: nx.Graph, mixer_angles: list[float], cost_angles: list[float]\n",
     ") -> Circuit:\n",
-    "    \n",
+    "\n",
     "    n_nodes = graph.number_of_nodes()\n",
     "\n",
     "    assert len(mixer_angles) == len(cost_angles)\n",
@@ -461,7 +461,7 @@
    "id": "bc2f8939-41b7-476b-a5a8-09de07211079",
    "metadata": {},
    "source": [
-    "We also need to extract our energy expectation values from a `BackendResult` object after our circuit is processed by the device/simulator. We do this with the `get_max_cut_energy` function below. Note that the fact that the maxcut Hamiltonian contains only commuting terms means that we do not need to calculate our energy expectation using multiple measurement circuits. This may not the the case for a different problem Hamiltonian."
+    "We also need to extract our energy expectation values from a `BackendResult` object after our circuit is processed by the device/simulator. We do this with the `energy_from_result` function below. Note that the fact that the maxcut Hamiltonian contains only commuting terms means that we do not need to calculate our energy expectation using multiple measurement circuits. This may not the the case for a different problem Hamiltonian."
    ]
   },
   {
@@ -475,10 +475,9 @@
     "\n",
     "\n",
     "def energy_from_result(graph: nx.Graph, results: BackendResult) -> float:\n",
-    "    edges = list(graph.edges)\n",
     "    energy = 0.0\n",
     "    dist = results.get_distribution()\n",
-    "    for i, j in edges:\n",
+    "    for i, j in graph.edges:\n",
     "        energy += sum((meas[i] ^ meas[j]) * prob for meas, prob in dist.items())\n",
     "\n",
     "    return energy"
@@ -506,7 +505,7 @@
     "    seed: int,\n",
     "    shots: int = 5000,\n",
     ") -> tuple[float, BackendResult]:\n",
-    "    \n",
+    "\n",
     "    # Build Circuit\n",
     "    qaoa_circuit = build_qaoa_circuit(\n",
     "        graph=graph, cost_angles=guess_cost_angles, mixer_angles=guess_mixer_angles\n",
@@ -545,20 +544,20 @@
    },
    "outputs": [],
    "source": [
-    "def optimise_qaoa_energy(\n",
+    "def solve_maxcut_instance(\n",
     "    graph: nx.Graph,\n",
     "    compiler_pass: Callable[[Circuit], bool],\n",
     "    backend: Backend,\n",
     "    iterations: int = 100,\n",
     "    p_value: int = 3,\n",
-    "    shots: int = 5000,\n",
+    "    n_shots: int = 5000,\n",
     "    seed: int = 12345,\n",
     ") -> tuple[BackendResult, np.array, np.array]:\n",
     "\n",
     "    highest_energy = 0\n",
     "    best_guess_mixer_angles = [0 for _ in range(p_value)]\n",
     "    best_guess_cost_angles = [0 for _ in range(p_value)]\n",
-    "    \n",
+    "\n",
     "    rng = np.random.default_rng(seed)\n",
     "\n",
     "    for _ in range(iterations):\n",
@@ -572,7 +571,7 @@
     "            guess_mixer_angles,\n",
     "            guess_cost_angles,\n",
     "            seed=seed,\n",
-    "            shots=shots,\n",
+    "            shots=n_shots,\n",
     "            graph=graph,\n",
     "        )\n",
     "\n",
@@ -633,10 +632,10 @@
    "outputs": [],
    "source": [
     "%%time\n",
-    "qaoa_result, cost_angles, mixer_angles = optimise_qaoa_energy(\n",
+    "qaoa_result, cost_angles, mixer_angles = solve_maxcut_instance(\n",
     "    backend=backend,\n",
     "    compiler_pass=backend.default_compilation_pass(2).apply,\n",
-    "    shots=5000,\n",
+    "    n_shots=5000,\n",
     "    iterations=100,\n",
     "    graph=max_cut_graph,\n",
     "    seed=12345,\n",

From 2bff90b559f99f01992b2214c06a32d4e77ee86f Mon Sep 17 00:00:00 2001
From: CalMacCQ <93673602+CalMacCQ@users.noreply.github.com>
Date: Mon, 23 Dec 2024 23:53:39 +0000
Subject: [PATCH 13/17] minor fixes

---
 .../pytket_qaoa_maxcut_example.ipynb          | 271 ++++++++++++++++--
 1 file changed, 252 insertions(+), 19 deletions(-)

diff --git a/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb b/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb
index 445d5477..1b98fd65 100644
--- a/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb
+++ b/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb
@@ -26,14 +26,25 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 1,
    "id": "9456fbeb",
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
     }
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "image/png": "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",
+      "text/plain": [
+       "<Figure size 200x200 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "import networkx as nx\n",
     "import matplotlib.pyplot as plt\n",
@@ -112,7 +123,7 @@
     "For the previous 3 vertex graph the *problem Hamiltonian* is\n",
     "\n",
     "$$\n",
-    "H_P = \\frac{1}{2} \\Big[ ( Z \\otimes Z \\otimes I ) + ( Z \\otimes I \\otimes Z ) + ( I \\otimes Z \\otimes Z ) \\Big]\n",
+    "H_P = \\frac{3}{2} I - \\frac{1}{2} \\Big[ ( Z \\otimes Z \\otimes I ) + ( Z \\otimes I \\otimes Z ) + ( I \\otimes Z \\otimes Z ) \\Big]\n",
     "$$\n",
     "\n",
     "where you will notice that there is a $ Z \\otimes Z$ acting between each vertex which is connected by an edge."
@@ -230,14 +241,25 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 3,
    "id": "688f1332",
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
     }
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "import networkx as nx\n",
     "\n",
@@ -331,14 +353,93 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 4,
    "id": "0a9db628",
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
     }
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "\n",
+       "\n",
+       "\n",
+       "\n",
+       "\n",
+       "\n",
+       "<div style=\"resize: vertical; overflow: auto; height: 300px; display: block\">\n",
+       "    <iframe srcdoc=\"\n",
+       "&lt;!DOCTYPE html&gt;\n",
+       "&lt;html lang=&#34;en&#34;&gt;\n",
+       "&lt;head&gt;\n",
+       "    &lt;meta charset=&#34;UTF-8&#34;&gt;\n",
+       "    &lt;!-- Download Vue 3--&gt;\n",
+       "&lt;script type=&#34;application/javascript&#34; src=&#34;https://cdn.jsdelivr.net/npm/vue@3&#34;&gt;&lt;/script&gt;\n",
+       "&lt;!-- Download Circuit Renderer with styles --&gt;\n",
+       "&lt;script type=&#34;application/javascript&#34; src=&#34;https://unpkg.com/pytket-circuit-renderer@0.10/dist/pytket-circuit-renderer.umd.js&#34;&gt;&lt;/script&gt;\n",
+       "&lt;link rel=&#34;stylesheet&#34; href=&#34;https://unpkg.com/pytket-circuit-renderer@0.10/dist/pytket-circuit-renderer.css&#34;&gt;\n",
+       "&lt;/head&gt;\n",
+       "&lt;body&gt;\n",
+       "\n",
+       "\n",
+       "    &lt;div id=&#34;circuit-display-vue-container-bd39f0d7-986d-46a1-877c-b435c37b5902&#34; class=&#34;pytket-circuit-display-container&#34;&gt;\n",
+       "        &lt;div style=&#34;display: none&#34;&gt;\n",
+       "            &lt;div id=&#34;circuit-json-to-display&#34;&gt;{&#34;bits&#34;: [], &#34;commands&#34;: [{&#34;args&#34;: [[&#34;q&#34;, [0]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [1]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [2]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [3]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [4]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [5]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [6]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}], &#34;created_qubits&#34;: [], &#34;discarded_qubits&#34;: [], &#34;implicit_permutation&#34;: [[[&#34;q&#34;, [0]], [&#34;q&#34;, [0]]], [[&#34;q&#34;, [1]], [&#34;q&#34;, [1]]], [[&#34;q&#34;, [2]], [&#34;q&#34;, [2]]], [[&#34;q&#34;, [3]], [&#34;q&#34;, [3]]], [[&#34;q&#34;, [4]], [&#34;q&#34;, [4]]], [[&#34;q&#34;, [5]], [&#34;q&#34;, [5]]], [[&#34;q&#34;, [6]], [&#34;q&#34;, [6]]]], &#34;phase&#34;: &#34;0.0&#34;, &#34;qubits&#34;: [[&#34;q&#34;, [0]], [&#34;q&#34;, [1]], [&#34;q&#34;, [2]], [&#34;q&#34;, [3]], [&#34;q&#34;, [4]], [&#34;q&#34;, [5]], [&#34;q&#34;, [6]]]}&lt;/div&gt;\n",
+       "        &lt;/div&gt;\n",
+       "        &lt;circuit-display-container\n",
+       "                :circuit-element-str=&#34;&#39;#circuit-json-to-display&#39;&#34;\n",
+       "                :init-render-options=&#34;initRenderOptions&#34;\n",
+       "                view-format=&#34;None&#34;\n",
+       "        &gt;&lt;/circuit-display-container&gt;\n",
+       "    &lt;/div&gt;\n",
+       "    &lt;script type=&#34;application/javascript&#34;&gt;\n",
+       "      const circuitRendererUid = &#34;bd39f0d7-986d-46a1-877c-b435c37b5902&#34;;\n",
+       "      const displayOptions = JSON.parse(&#39;{&#34;zxStyle&#34;: true, &#34;condenseCBits&#34;: false}&#39;);\n",
+       "\n",
+       "      // Script to initialise the circuit renderer app\n",
+       "\n",
+       "const { createApp } = Vue;\n",
+       "const circuitDisplayContainer = window[&#34;pytket-circuit-renderer&#34;].default;\n",
+       "// Init variables to be shared between circuit display instances\n",
+       "if (typeof window.pytketCircuitDisplays === &#34;undefined&#34;) {\n",
+       "    window.pytketCircuitDisplays = {};\n",
+       "}\n",
+       "// Create the root Vue component\n",
+       "const app = createApp({\n",
+       "    delimiters: [&#39;[[#&#39;, &#39;#]]&#39;],\n",
+       "    components: { circuitDisplayContainer },\n",
+       "    data () {\n",
+       "      return {\n",
+       "        initRenderOptions: displayOptions,\n",
+       "      }\n",
+       "    }\n",
+       "})\n",
+       "app.config.unwrapInjectedRef = true;\n",
+       "app.mount(&#34;#circuit-display-vue-container-&#34;+circuitRendererUid);\n",
+       "window.pytketCircuitDisplays[circuitRendererUid] = app;\n",
+       "    &lt;/script&gt;\n",
+       "\n",
+       "\n",
+       "\n",
+       "&lt;/body&gt;\n",
+       "&lt;/html&gt;\n",
+       "\"\n",
+       "            width=\"100%\" height=\"100%\"\n",
+       "            style=\"border: none; outline: none; overflow: auto\"></iframe>\n",
+       "</div>\n",
+       "\n"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "from pytket import Circuit\n",
     "from pytket.circuit.display import render_circuit_jupyter as draw\n",
@@ -381,7 +482,7 @@
     "def build_cost_layer(graph: nx.Graph, gamma_val: float) -> Circuit:\n",
     "    circ = Circuit(graph.number_of_nodes())\n",
     "\n",
-    "    for i, j in list(graph.edges):\n",
+    "    for i, j in graph.edges:\n",
     "        circ.ZZPhase(-gamma_val / 2, i, j)\n",
     "\n",
     "    return circ"
@@ -444,10 +545,89 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 8,
    "id": "f97de321",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "\n",
+       "\n",
+       "\n",
+       "\n",
+       "\n",
+       "\n",
+       "<div style=\"resize: vertical; overflow: auto; height: 300px; display: block\">\n",
+       "    <iframe srcdoc=\"\n",
+       "&lt;!DOCTYPE html&gt;\n",
+       "&lt;html lang=&#34;en&#34;&gt;\n",
+       "&lt;head&gt;\n",
+       "    &lt;meta charset=&#34;UTF-8&#34;&gt;\n",
+       "    &lt;!-- Download Vue 3--&gt;\n",
+       "&lt;script type=&#34;application/javascript&#34; src=&#34;https://cdn.jsdelivr.net/npm/vue@3&#34;&gt;&lt;/script&gt;\n",
+       "&lt;!-- Download Circuit Renderer with styles --&gt;\n",
+       "&lt;script type=&#34;application/javascript&#34; src=&#34;https://unpkg.com/pytket-circuit-renderer@0.10/dist/pytket-circuit-renderer.umd.js&#34;&gt;&lt;/script&gt;\n",
+       "&lt;link rel=&#34;stylesheet&#34; href=&#34;https://unpkg.com/pytket-circuit-renderer@0.10/dist/pytket-circuit-renderer.css&#34;&gt;\n",
+       "&lt;/head&gt;\n",
+       "&lt;body&gt;\n",
+       "\n",
+       "\n",
+       "    &lt;div id=&#34;circuit-display-vue-container-622bbb86-e072-4d05-b32a-7656d0a18c2f&#34; class=&#34;pytket-circuit-display-container&#34;&gt;\n",
+       "        &lt;div style=&#34;display: none&#34;&gt;\n",
+       "            &lt;div id=&#34;circuit-json-to-display&#34;&gt;{&#34;bits&#34;: [[&#34;c&#34;, [0]], [&#34;c&#34;, [1]], [&#34;c&#34;, [2]]], &#34;commands&#34;: [{&#34;args&#34;: [[&#34;q&#34;, [0]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [1]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [2]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [0]], [&#34;q&#34;, [1]]], &#34;op&#34;: {&#34;params&#34;: [&#34;-0.375&#34;], &#34;type&#34;: &#34;ZZPhase&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [1]], [&#34;q&#34;, [2]]], &#34;op&#34;: {&#34;params&#34;: [&#34;-0.375&#34;], &#34;type&#34;: &#34;ZZPhase&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [0]], [&#34;q&#34;, [1]], [&#34;q&#34;, [2]]], &#34;op&#34;: {&#34;data&#34;: &#34;&#34;, &#34;signature&#34;: [&#34;Q&#34;, &#34;Q&#34;, &#34;Q&#34;], &#34;type&#34;: &#34;Barrier&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [0]]], &#34;op&#34;: {&#34;params&#34;: [&#34;0.8&#34;], &#34;type&#34;: &#34;Rx&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [1]]], &#34;op&#34;: {&#34;params&#34;: [&#34;0.8&#34;], &#34;type&#34;: &#34;Rx&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [2]]], &#34;op&#34;: {&#34;params&#34;: [&#34;0.8&#34;], &#34;type&#34;: &#34;Rx&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [0]], [&#34;q&#34;, [1]]], &#34;op&#34;: {&#34;params&#34;: [&#34;-0.3&#34;], &#34;type&#34;: &#34;ZZPhase&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [1]], [&#34;q&#34;, [2]]], &#34;op&#34;: {&#34;params&#34;: [&#34;-0.3&#34;], &#34;type&#34;: &#34;ZZPhase&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [0]], [&#34;q&#34;, [1]], [&#34;q&#34;, [2]]], &#34;op&#34;: {&#34;data&#34;: &#34;&#34;, &#34;signature&#34;: [&#34;Q&#34;, &#34;Q&#34;, &#34;Q&#34;], &#34;type&#34;: &#34;Barrier&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [0]]], &#34;op&#34;: {&#34;params&#34;: [&#34;0.1&#34;], &#34;type&#34;: &#34;Rx&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [1]]], &#34;op&#34;: {&#34;params&#34;: [&#34;0.1&#34;], &#34;type&#34;: &#34;Rx&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [2]]], &#34;op&#34;: {&#34;params&#34;: [&#34;0.1&#34;], &#34;type&#34;: &#34;Rx&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [0]], [&#34;c&#34;, [0]]], &#34;op&#34;: {&#34;type&#34;: &#34;Measure&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [1]], [&#34;c&#34;, [1]]], &#34;op&#34;: {&#34;type&#34;: &#34;Measure&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [2]], [&#34;c&#34;, [2]]], &#34;op&#34;: {&#34;type&#34;: &#34;Measure&#34;}}], &#34;created_qubits&#34;: [], &#34;discarded_qubits&#34;: [], &#34;implicit_permutation&#34;: [[[&#34;q&#34;, [0]], [&#34;q&#34;, [0]]], [[&#34;q&#34;, [1]], [&#34;q&#34;, [1]]], [[&#34;q&#34;, [2]], [&#34;q&#34;, [2]]]], &#34;phase&#34;: &#34;0.0&#34;, &#34;qubits&#34;: [[&#34;q&#34;, [0]], [&#34;q&#34;, [1]], [&#34;q&#34;, [2]]]}&lt;/div&gt;\n",
+       "        &lt;/div&gt;\n",
+       "        &lt;circuit-display-container\n",
+       "                :circuit-element-str=&#34;&#39;#circuit-json-to-display&#39;&#34;\n",
+       "                :init-render-options=&#34;initRenderOptions&#34;\n",
+       "                view-format=&#34;None&#34;\n",
+       "        &gt;&lt;/circuit-display-container&gt;\n",
+       "    &lt;/div&gt;\n",
+       "    &lt;script type=&#34;application/javascript&#34;&gt;\n",
+       "      const circuitRendererUid = &#34;622bbb86-e072-4d05-b32a-7656d0a18c2f&#34;;\n",
+       "      const displayOptions = JSON.parse(&#39;{&#34;zxStyle&#34;: true, &#34;condenseCBits&#34;: false}&#39;);\n",
+       "\n",
+       "      // Script to initialise the circuit renderer app\n",
+       "\n",
+       "const { createApp } = Vue;\n",
+       "const circuitDisplayContainer = window[&#34;pytket-circuit-renderer&#34;].default;\n",
+       "// Init variables to be shared between circuit display instances\n",
+       "if (typeof window.pytketCircuitDisplays === &#34;undefined&#34;) {\n",
+       "    window.pytketCircuitDisplays = {};\n",
+       "}\n",
+       "// Create the root Vue component\n",
+       "const app = createApp({\n",
+       "    delimiters: [&#39;[[#&#39;, &#39;#]]&#39;],\n",
+       "    components: { circuitDisplayContainer },\n",
+       "    data () {\n",
+       "      return {\n",
+       "        initRenderOptions: displayOptions,\n",
+       "      }\n",
+       "    }\n",
+       "})\n",
+       "app.config.unwrapInjectedRef = true;\n",
+       "app.mount(&#34;#circuit-display-vue-container-&#34;+circuitRendererUid);\n",
+       "window.pytketCircuitDisplays[circuitRendererUid] = app;\n",
+       "    &lt;/script&gt;\n",
+       "\n",
+       "\n",
+       "\n",
+       "&lt;/body&gt;\n",
+       "&lt;/html&gt;\n",
+       "\"\n",
+       "            width=\"100%\" height=\"100%\"\n",
+       "            style=\"border: none; outline: none; overflow: auto\"></iframe>\n",
+       "</div>\n",
+       "\n"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "from networkx import path_graph\n",
     "\n",
@@ -561,10 +741,8 @@
     "    rng = np.random.default_rng(seed)\n",
     "\n",
     "    for _ in range(iterations):\n",
-    "\n",
     "        guess_mixer_angles = rng.uniform(0, 1, p_value)\n",
     "        guess_cost_angles = rng.uniform(0, 1, p_value)\n",
-    "\n",
     "        qaoa_energy, result = eval_qaoa_energy(\n",
     "            backend,\n",
     "            compiler_pass,\n",
@@ -576,7 +754,6 @@
     "        )\n",
     "\n",
     "        if qaoa_energy > highest_energy:\n",
-    "\n",
     "            print(\"new highest energy found: \", qaoa_energy)\n",
     "\n",
     "            best_guess_mixer_angles = np.round(guess_mixer_angles, 3)\n",
@@ -622,14 +799,31 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 13,
    "id": "aaea7e2f",
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
     }
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "new highest energy found:  3.1432\n",
+      "new highest energy found:  3.283599999999999\n",
+      "new highest energy found:  4.361\n",
+      "new highest energy found:  4.925600000000001\n",
+      "new highest energy found:  4.941999999999999\n",
+      "highest energy:  4.941999999999999\n",
+      "best guess mixer angles:  [0.392 0.247 0.138]\n",
+      "best guess cost angles:  [0.592 0.738 0.608]\n",
+      "CPU times: user 2min 17s, sys: 33.2 s, total: 2min 50s\n",
+      "Wall time: 43.2 s\n"
+     ]
+    }
+   ],
    "source": [
     "%%time\n",
     "qaoa_result, cost_angles, mixer_angles = solve_maxcut_instance(\n",
@@ -644,10 +838,28 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 14,
    "id": "3b86301e-7645-4553-be38-3ebf89eedd37",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Success ratio 0.4246 \n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "import matplotlib.pyplot as plt\n",
     "\n",
@@ -694,10 +906,31 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 15,
    "id": "ffce2a97-902c-44d8-8d64-b25498752907",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "G = nx.Graph()\n",
     "G.add_edges_from(max_cut_graph_edges)\n",

From 0389602c7539995de45900d51371770f667afa6a Mon Sep 17 00:00:00 2001
From: CalMacCQ <93673602+CalMacCQ@users.noreply.github.com>
Date: Tue, 24 Dec 2024 00:36:50 +0000
Subject: [PATCH 14/17] fix errors in cost function equations

---
 .../pytket_qaoa_maxcut_example.ipynb          | 296 ++----------------
 1 file changed, 18 insertions(+), 278 deletions(-)

diff --git a/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb b/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb
index 1b98fd65..14e15297 100644
--- a/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb
+++ b/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb
@@ -26,25 +26,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": null,
    "id": "9456fbeb",
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
     }
    },
-   "outputs": [
-    {
-     "data": {
-      "image/png": "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",
-      "text/plain": [
-       "<Figure size 200x200 with 1 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "import networkx as nx\n",
     "import matplotlib.pyplot as plt\n",
@@ -98,19 +87,6 @@
     "with $H_P$ depending on the problem instance. "
    ]
   },
-  {
-   "cell_type": "markdown",
-   "id": "3596e66d",
-   "metadata": {},
-   "source": [
-    "## Cost function for Maxcut\n",
-    "$$\n",
-    "\\begin{equation}\n",
-    "C= \\sum_{(i,\\,j)} x_i(1-x_j)\n",
-    "\\end{equation}\n",
-    "$$"
-   ]
-  },
   {
    "cell_type": "markdown",
    "id": "d720b387",
@@ -160,19 +136,17 @@
     "\n",
     "$$\n",
     "\\begin{equation}\n",
-    "C= \\sum_{(i,j)} x_i(1-x_j)\n",
+    "C= \\frac{1}{2}\\sum_{(i,j)} (1-z_i\\,z_j)\n",
     "\\end{equation}\n",
     "$$\n",
     "\n",
-    "Here $x_i$ and $x_j$ are the the \"colours\" of each vertex.  \n",
+    "Here $z_i$ and $z_j$ are the the \"colours\" of each vertex.  \n",
     "\n",
     "$$\n",
     "\\begin{equation}\n",
-    "x_i,x_j \\in \\{0,1\\}\n",
+    "z_i,z_j \\in \\{0,1\\}\n",
     "\\end{equation}\n",
-    "$$\n",
-    "\n",
-    "$x_i(1-x_j)=0$ if $x_i=x_j$ and $ x_i(1-x_j)=1$ if the terms are not equal."
+    "$$"
    ]
   },
   {
@@ -184,15 +158,6 @@
     }
    },
    "source": [
-    "We want to encode our Maxcut cost function as a Hamiltonain. To do this we can perform the following translation.\n",
-    "\n",
-    "$$\n",
-    "\\begin{equation}\n",
-    "x_i \\mapsto \\frac{1}{2}(I-Z_i)\n",
-    "\\end{equation}\n",
-    "$$\n",
-    "\n",
-    "\n",
     "The Pauli Z operator can be used to distinguish between the $|0\\rangle$ and $|1\\rangle$ basis states as these are eigenstates with eigenvalues $\\pm 1$ .\n",
     "\n",
     "$$\n",
@@ -241,25 +206,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": null,
    "id": "688f1332",
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
     }
    },
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "import networkx as nx\n",
     "\n",
@@ -353,93 +307,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": null,
    "id": "0a9db628",
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
     }
    },
-   "outputs": [
-    {
-     "data": {
-      "text/html": [
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "<div style=\"resize: vertical; overflow: auto; height: 300px; display: block\">\n",
-       "    <iframe srcdoc=\"\n",
-       "&lt;!DOCTYPE html&gt;\n",
-       "&lt;html lang=&#34;en&#34;&gt;\n",
-       "&lt;head&gt;\n",
-       "    &lt;meta charset=&#34;UTF-8&#34;&gt;\n",
-       "    &lt;!-- Download Vue 3--&gt;\n",
-       "&lt;script type=&#34;application/javascript&#34; src=&#34;https://cdn.jsdelivr.net/npm/vue@3&#34;&gt;&lt;/script&gt;\n",
-       "&lt;!-- Download Circuit Renderer with styles --&gt;\n",
-       "&lt;script type=&#34;application/javascript&#34; src=&#34;https://unpkg.com/pytket-circuit-renderer@0.10/dist/pytket-circuit-renderer.umd.js&#34;&gt;&lt;/script&gt;\n",
-       "&lt;link rel=&#34;stylesheet&#34; href=&#34;https://unpkg.com/pytket-circuit-renderer@0.10/dist/pytket-circuit-renderer.css&#34;&gt;\n",
-       "&lt;/head&gt;\n",
-       "&lt;body&gt;\n",
-       "\n",
-       "\n",
-       "    &lt;div id=&#34;circuit-display-vue-container-bd39f0d7-986d-46a1-877c-b435c37b5902&#34; class=&#34;pytket-circuit-display-container&#34;&gt;\n",
-       "        &lt;div style=&#34;display: none&#34;&gt;\n",
-       "            &lt;div id=&#34;circuit-json-to-display&#34;&gt;{&#34;bits&#34;: [], &#34;commands&#34;: [{&#34;args&#34;: [[&#34;q&#34;, [0]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [1]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [2]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [3]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [4]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [5]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [6]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}], &#34;created_qubits&#34;: [], &#34;discarded_qubits&#34;: [], &#34;implicit_permutation&#34;: [[[&#34;q&#34;, [0]], [&#34;q&#34;, [0]]], [[&#34;q&#34;, [1]], [&#34;q&#34;, [1]]], [[&#34;q&#34;, [2]], [&#34;q&#34;, [2]]], [[&#34;q&#34;, [3]], [&#34;q&#34;, [3]]], [[&#34;q&#34;, [4]], [&#34;q&#34;, [4]]], [[&#34;q&#34;, [5]], [&#34;q&#34;, [5]]], [[&#34;q&#34;, [6]], [&#34;q&#34;, [6]]]], &#34;phase&#34;: &#34;0.0&#34;, &#34;qubits&#34;: [[&#34;q&#34;, [0]], [&#34;q&#34;, [1]], [&#34;q&#34;, [2]], [&#34;q&#34;, [3]], [&#34;q&#34;, [4]], [&#34;q&#34;, [5]], [&#34;q&#34;, [6]]]}&lt;/div&gt;\n",
-       "        &lt;/div&gt;\n",
-       "        &lt;circuit-display-container\n",
-       "                :circuit-element-str=&#34;&#39;#circuit-json-to-display&#39;&#34;\n",
-       "                :init-render-options=&#34;initRenderOptions&#34;\n",
-       "                view-format=&#34;None&#34;\n",
-       "        &gt;&lt;/circuit-display-container&gt;\n",
-       "    &lt;/div&gt;\n",
-       "    &lt;script type=&#34;application/javascript&#34;&gt;\n",
-       "      const circuitRendererUid = &#34;bd39f0d7-986d-46a1-877c-b435c37b5902&#34;;\n",
-       "      const displayOptions = JSON.parse(&#39;{&#34;zxStyle&#34;: true, &#34;condenseCBits&#34;: false}&#39;);\n",
-       "\n",
-       "      // Script to initialise the circuit renderer app\n",
-       "\n",
-       "const { createApp } = Vue;\n",
-       "const circuitDisplayContainer = window[&#34;pytket-circuit-renderer&#34;].default;\n",
-       "// Init variables to be shared between circuit display instances\n",
-       "if (typeof window.pytketCircuitDisplays === &#34;undefined&#34;) {\n",
-       "    window.pytketCircuitDisplays = {};\n",
-       "}\n",
-       "// Create the root Vue component\n",
-       "const app = createApp({\n",
-       "    delimiters: [&#39;[[#&#39;, &#39;#]]&#39;],\n",
-       "    components: { circuitDisplayContainer },\n",
-       "    data () {\n",
-       "      return {\n",
-       "        initRenderOptions: displayOptions,\n",
-       "      }\n",
-       "    }\n",
-       "})\n",
-       "app.config.unwrapInjectedRef = true;\n",
-       "app.mount(&#34;#circuit-display-vue-container-&#34;+circuitRendererUid);\n",
-       "window.pytketCircuitDisplays[circuitRendererUid] = app;\n",
-       "    &lt;/script&gt;\n",
-       "\n",
-       "\n",
-       "\n",
-       "&lt;/body&gt;\n",
-       "&lt;/html&gt;\n",
-       "\"\n",
-       "            width=\"100%\" height=\"100%\"\n",
-       "            style=\"border: none; outline: none; overflow: auto\"></iframe>\n",
-       "</div>\n",
-       "\n"
-      ],
-      "text/plain": [
-       "<IPython.core.display.HTML object>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "from pytket import Circuit\n",
     "from pytket.circuit.display import render_circuit_jupyter as draw\n",
@@ -545,89 +420,10 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": null,
    "id": "f97de321",
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/html": [
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "<div style=\"resize: vertical; overflow: auto; height: 300px; display: block\">\n",
-       "    <iframe srcdoc=\"\n",
-       "&lt;!DOCTYPE html&gt;\n",
-       "&lt;html lang=&#34;en&#34;&gt;\n",
-       "&lt;head&gt;\n",
-       "    &lt;meta charset=&#34;UTF-8&#34;&gt;\n",
-       "    &lt;!-- Download Vue 3--&gt;\n",
-       "&lt;script type=&#34;application/javascript&#34; src=&#34;https://cdn.jsdelivr.net/npm/vue@3&#34;&gt;&lt;/script&gt;\n",
-       "&lt;!-- Download Circuit Renderer with styles --&gt;\n",
-       "&lt;script type=&#34;application/javascript&#34; src=&#34;https://unpkg.com/pytket-circuit-renderer@0.10/dist/pytket-circuit-renderer.umd.js&#34;&gt;&lt;/script&gt;\n",
-       "&lt;link rel=&#34;stylesheet&#34; href=&#34;https://unpkg.com/pytket-circuit-renderer@0.10/dist/pytket-circuit-renderer.css&#34;&gt;\n",
-       "&lt;/head&gt;\n",
-       "&lt;body&gt;\n",
-       "\n",
-       "\n",
-       "    &lt;div id=&#34;circuit-display-vue-container-622bbb86-e072-4d05-b32a-7656d0a18c2f&#34; class=&#34;pytket-circuit-display-container&#34;&gt;\n",
-       "        &lt;div style=&#34;display: none&#34;&gt;\n",
-       "            &lt;div id=&#34;circuit-json-to-display&#34;&gt;{&#34;bits&#34;: [[&#34;c&#34;, [0]], [&#34;c&#34;, [1]], [&#34;c&#34;, [2]]], &#34;commands&#34;: [{&#34;args&#34;: [[&#34;q&#34;, [0]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [1]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [2]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [0]], [&#34;q&#34;, [1]]], &#34;op&#34;: {&#34;params&#34;: [&#34;-0.375&#34;], &#34;type&#34;: &#34;ZZPhase&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [1]], [&#34;q&#34;, [2]]], &#34;op&#34;: {&#34;params&#34;: [&#34;-0.375&#34;], &#34;type&#34;: &#34;ZZPhase&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [0]], [&#34;q&#34;, [1]], [&#34;q&#34;, [2]]], &#34;op&#34;: {&#34;data&#34;: &#34;&#34;, &#34;signature&#34;: [&#34;Q&#34;, &#34;Q&#34;, &#34;Q&#34;], &#34;type&#34;: &#34;Barrier&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [0]]], &#34;op&#34;: {&#34;params&#34;: [&#34;0.8&#34;], &#34;type&#34;: &#34;Rx&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [1]]], &#34;op&#34;: {&#34;params&#34;: [&#34;0.8&#34;], &#34;type&#34;: &#34;Rx&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [2]]], &#34;op&#34;: {&#34;params&#34;: [&#34;0.8&#34;], &#34;type&#34;: &#34;Rx&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [0]], [&#34;q&#34;, [1]]], &#34;op&#34;: {&#34;params&#34;: [&#34;-0.3&#34;], &#34;type&#34;: &#34;ZZPhase&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [1]], [&#34;q&#34;, [2]]], &#34;op&#34;: {&#34;params&#34;: [&#34;-0.3&#34;], &#34;type&#34;: &#34;ZZPhase&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [0]], [&#34;q&#34;, [1]], [&#34;q&#34;, [2]]], &#34;op&#34;: {&#34;data&#34;: &#34;&#34;, &#34;signature&#34;: [&#34;Q&#34;, &#34;Q&#34;, &#34;Q&#34;], &#34;type&#34;: &#34;Barrier&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [0]]], &#34;op&#34;: {&#34;params&#34;: [&#34;0.1&#34;], &#34;type&#34;: &#34;Rx&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [1]]], &#34;op&#34;: {&#34;params&#34;: [&#34;0.1&#34;], &#34;type&#34;: &#34;Rx&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [2]]], &#34;op&#34;: {&#34;params&#34;: [&#34;0.1&#34;], &#34;type&#34;: &#34;Rx&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [0]], [&#34;c&#34;, [0]]], &#34;op&#34;: {&#34;type&#34;: &#34;Measure&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [1]], [&#34;c&#34;, [1]]], &#34;op&#34;: {&#34;type&#34;: &#34;Measure&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [2]], [&#34;c&#34;, [2]]], &#34;op&#34;: {&#34;type&#34;: &#34;Measure&#34;}}], &#34;created_qubits&#34;: [], &#34;discarded_qubits&#34;: [], &#34;implicit_permutation&#34;: [[[&#34;q&#34;, [0]], [&#34;q&#34;, [0]]], [[&#34;q&#34;, [1]], [&#34;q&#34;, [1]]], [[&#34;q&#34;, [2]], [&#34;q&#34;, [2]]]], &#34;phase&#34;: &#34;0.0&#34;, &#34;qubits&#34;: [[&#34;q&#34;, [0]], [&#34;q&#34;, [1]], [&#34;q&#34;, [2]]]}&lt;/div&gt;\n",
-       "        &lt;/div&gt;\n",
-       "        &lt;circuit-display-container\n",
-       "                :circuit-element-str=&#34;&#39;#circuit-json-to-display&#39;&#34;\n",
-       "                :init-render-options=&#34;initRenderOptions&#34;\n",
-       "                view-format=&#34;None&#34;\n",
-       "        &gt;&lt;/circuit-display-container&gt;\n",
-       "    &lt;/div&gt;\n",
-       "    &lt;script type=&#34;application/javascript&#34;&gt;\n",
-       "      const circuitRendererUid = &#34;622bbb86-e072-4d05-b32a-7656d0a18c2f&#34;;\n",
-       "      const displayOptions = JSON.parse(&#39;{&#34;zxStyle&#34;: true, &#34;condenseCBits&#34;: false}&#39;);\n",
-       "\n",
-       "      // Script to initialise the circuit renderer app\n",
-       "\n",
-       "const { createApp } = Vue;\n",
-       "const circuitDisplayContainer = window[&#34;pytket-circuit-renderer&#34;].default;\n",
-       "// Init variables to be shared between circuit display instances\n",
-       "if (typeof window.pytketCircuitDisplays === &#34;undefined&#34;) {\n",
-       "    window.pytketCircuitDisplays = {};\n",
-       "}\n",
-       "// Create the root Vue component\n",
-       "const app = createApp({\n",
-       "    delimiters: [&#39;[[#&#39;, &#39;#]]&#39;],\n",
-       "    components: { circuitDisplayContainer },\n",
-       "    data () {\n",
-       "      return {\n",
-       "        initRenderOptions: displayOptions,\n",
-       "      }\n",
-       "    }\n",
-       "})\n",
-       "app.config.unwrapInjectedRef = true;\n",
-       "app.mount(&#34;#circuit-display-vue-container-&#34;+circuitRendererUid);\n",
-       "window.pytketCircuitDisplays[circuitRendererUid] = app;\n",
-       "    &lt;/script&gt;\n",
-       "\n",
-       "\n",
-       "\n",
-       "&lt;/body&gt;\n",
-       "&lt;/html&gt;\n",
-       "\"\n",
-       "            width=\"100%\" height=\"100%\"\n",
-       "            style=\"border: none; outline: none; overflow: auto\"></iframe>\n",
-       "</div>\n",
-       "\n"
-      ],
-      "text/plain": [
-       "<IPython.core.display.HTML object>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "from networkx import path_graph\n",
     "\n",
@@ -799,31 +595,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": null,
    "id": "aaea7e2f",
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
     }
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "new highest energy found:  3.1432\n",
-      "new highest energy found:  3.283599999999999\n",
-      "new highest energy found:  4.361\n",
-      "new highest energy found:  4.925600000000001\n",
-      "new highest energy found:  4.941999999999999\n",
-      "highest energy:  4.941999999999999\n",
-      "best guess mixer angles:  [0.392 0.247 0.138]\n",
-      "best guess cost angles:  [0.592 0.738 0.608]\n",
-      "CPU times: user 2min 17s, sys: 33.2 s, total: 2min 50s\n",
-      "Wall time: 43.2 s\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "%%time\n",
     "qaoa_result, cost_angles, mixer_angles = solve_maxcut_instance(\n",
@@ -838,28 +617,10 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": null,
    "id": "3b86301e-7645-4553-be38-3ebf89eedd37",
    "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Success ratio 0.4246 \n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "import matplotlib.pyplot as plt\n",
     "\n",
@@ -906,31 +667,10 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": null,
    "id": "ffce2a97-902c-44d8-8d64-b25498752907",
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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EuhYvXqzHH39cy5YtU6tWrUzHAQAg+0RHS5Urp/rtNXIUym6S6v3te49IKpbWuf39pePHHdNKL0OhRLrsdrsaN26spKQkhYeHM6UEAHivd96RRo5M9SGcNXIUylmS2mb23Far9OGHjiWIvAxPeSNdFotFYWFhioyM1MKFC03HAQAg+/z0U4af6I6T9M+L4mmw2Rzn90JMKJEhdrtdzZs318WLF7V161ZZrfwsAgDwMpcvp/vQzBo5JpT5JF2R5CfpAUnDJNXNyGcEBUlXrjjuqfQitAJkyM0p5Y4dO9iOEQDgnfbuTfeQQEnPShohab6kDyX9Jkep3JaRz7h+XTp8OMsR3RUTSmRK69at9fvvv+u3336Tn5f9dAUA8HGrV2dprciDkmpKelDS0oy8YccOqWbNTH+OO2NCiUwJCwvT3r17NWPGDNNRAABwrYCALL2toqSnJK2WlKG7LwMDs/Q57owJJTLtySef1N69e7V37175+/ubjgMAgGscP+7YfzsLestxH+UlSQXSOtBqleLipDx5svQ57ooJJTItNDRUBw8e1OTJk01HAQDAdUqXlooWzdJbYyQFyfGwTpoqVvS6MilRKJEF999/v9q2bavQ0FAlJCSYjgMAgGtYLI57KNO4+nbmNq/tkPSzpFZKp1j5+0stWzoV0V1xyRtZsmfPHlWvXl2jR49W586dTccBAMA1Vq5Ms/S1kJRbUiNJJSTtkTROUoAcWy9WTe/827dLtWq5IqlboVAiy/7zn/9o9erVOnjwoHLnzm06DgAAzrPbpapVpYMHb7vA+UhJ0+R4svuypOKSHpL0gRwP56TKz09q0EDasMH1md0AhRJZduDAAVWtWlWfffaZunfvbjoOAACusXGj1KSJo1y6ir+/Y7mgatVcd043wj2UyLJKlSqpQ4cOGjJkiOLj403HAQDANRo1knr1ctxT6SoffeS1ZVKiUMJJAwYM0IULFzRq1CjTUQAAcJ2PP1bSM8/I5opzvfGGo6B6MQolnHLPPfeoU6dOGjp0qC5fvmw6DgAALmGzWNTeYtE3N3eFy+zucH5+jgnnBx9IX3/t2mmnG6JQwmnvv/++4uPj9eWXX5qOAgCAS4SGhurH2bNVetYsadUq6c47Hd9Ir1je/H7FitLmzdKgQV5fJiUKJVzgzjvvVOfOnTV8+HCdP3/edBwAAJwyY8YMDR48WB9//LGefvppqXlz6dAhae5cqWnT1LdozJVLat1aWrxY2rNHCgnJ2eAG8ZQ3XOKPP/5Q+fLl1b17d3300Uem4wAAkCURERFq2rSp2rZtq8mTJ8tyu+liYqK0e7cUHS3duCEFBTmWGqpSJc1F0b0ZhRIu07dvX40aNUqxsbEqXry46TgAAGTKsWPHFBISorJly2r16tUKCgoyHcljcMkbLtOrVy9ZrVZ9+umnpqMAAJAp8fHxeuqpp+Tv76+ffvqJMplJFEq4TNGiRdWjRw+NHj1aJ06cMB0HAIAMsdls6tChg/bv368FCxaoZMmSpiN5HAolXKpHjx7KnTu3hgwZYjoKAAAZMmjQIM2dO1fTpk1TLS/cZzsnUCjhUoUKFVLPnj01btw4HT161HQcAADSNH36dIWFhWnIkCF66qmnTMfxWDyUA5e7cuWKypUrp6efflrjxo0zHQcAgNsKDw9X06ZN9fzzz2vixIm3f6IbGUKhRLYYPny4+vbtq3379qlChQqm4wAAkMLvv/+ukJAQlS9fXqtWrVKuXLlMR/JoFEpki6tXr6pixYp6+OGHNWnSJNNxAAC4JT4+Xk2aNNH58+cVGRmpEiVKmI7k8biHEtkiT5486tevn6ZOnap9+/aZjgMAgCTHE90vvfSSDh48qAULFlAmXYQJJbLNjRs3VKlSJTVq1EgzZswwHQcAAPXv318ff/yx5s+frzZt2piO4zWYUCLb5MqVSwMGDNDMmTO1c+dO03EAAD5u2rRp+uijj/Tpp59SJl2MCSWyVWJioqpUqaKaNWtq3rx5puMAAHzU5s2b1axZM73wwgv6/vvveaLbxSiUyHaTJ09Whw4dFBUVpeDgYNNxAAA+5ujRowoJCVGlSpW0YsUKnujOBhRKZLvk5GRVr15d5cqV0+LFi03HAQD4kCtXrqhJkya6dOmSIiIiVLx4cdORvBL3UCLb+fn5adCgQVqyZIk2btxoOg4AwEfcfKL70KFDWrBgAWUyGzGhRI6w2Wy6//77Vbx4ca1cudJ0HACAD+jXr58++eQT/fzzz3riiSdMx/FqTCiRI6xWq0JDQ7Vq1SqtXr3adBwAgJebMmWKhgwZomHDhlEmcwATSuQYu92uevXqKSgoSOvXr+cJOwBAtti0aZOaNWum9u3ba/z48fz3JgdQKJGjlixZoscee0xLly5V69atTccBAHiZI0eOKCQkRJUrV9by5ct5ojuHUCiRo+x2uxo3bqzExERFRETwUyMAwGWuXLmixo0bKy4uTuHh4TyEk4O4hxI5ymKx6MMPP1RUVJQWLFhgOg4AwEvYbDa1b99esbGxPNFtABNKGNG8eXOdP39e27Ztk9XKzzUAAOf07dtXw4YN04IFC/TYY4+ZjuNz+C85jAgLC9POnTs1Z84c01EAAB5u0qRJ+vTTT/XZZ59RJg1hQgljHnnkER09elS//fab/Pz8TMcBAHigX3/9VS1atNBLL72kb7/9lnvzDaFQwpjIyEiFhIRoypQp+s9//mM6DgDAwxw+fFghISGqWrWqli9frsDAQNORfBaFEkY99dRT2r17t/bu3auAgADTcQAAHiIuLk6NGjXS1atXFR4ermLFipmO5NO4hxJGhYaG6tChQ5o8ebLpKAAAD5GcnKwXX3xRR48e1YIFCyiTboAJJYxr166dwsPDFR0dzQK0AIB09e7dW8OHD9fChQv16KOPmo4DMaGEGxg8eLCOHTum8ePHm44CAHBzEydO1LBhw/T5559TJt0IE0q4hZdeekkrV67UoUOHlDt3btNxAABuaMOGDWrRooU6duyosWPH8kS3G6FQwi0cPHhQVapU0bBhw9SjRw/TcQAAbiY2NlYhISGqXr26li1bxhPdboZCCbfRqVMn/fzzz4qJiVG+fPlMxwEAuInLly+rUaNGun79usLDw1W0aFHTkfA3FEq4jSNHjqhSpUoKDQ3Vf//bVz/+KEVEOL7OnpXsdqlYMSkkxPH13HNSyZKmUwMAslNycrKeeuoprV+/Xps3b1bVqlVNR8JtUCjhVv7znw/044/VZbe3VXKyRX5+UlJSymP8/SWbTbJapbZtpcGDpXvvNZMXAJC9evbsqS+++EKLFy9W69atTcdBKiiUcAs2mzRqlNSrl10JCUmSMrbIub+/o1gOGSK9/bbEDo4A4D3Gjx+vTp06aeTIkeratavpOEgDhRLGJSVJHTtK06Y5d5527aSpUyU23AEAz7du3Tq1bNlSr776qr755hue6HZzFEoYZbdLr7wiTZ7s+GtnWCzSv//tKKb8ewcAPFdMTIxCQkJUq1YtLV26lK15PQCFEkZNmSK9/LJrzzl+vPTqq649JwAgZ1y+fFkNGzZUQkKCwsPDVaRIEdORkAEUShhz6pTjYZorV9KaTl6RNExSuKQISRckTZDUMdXz5s0r7dsnlSnj2rwAgOyVnJysNm3aaOPGjdq8ebOqVKliOhIyiK0XYcxXX0lXr6Z3qfuspFBJeyXVytB5r1+XRo50Ph8AIGf16tVLv/zyi2bNmkWZ9DBMKGHEjRtS6dLS+fPpHinHVLKUpChJ9ZTehFKSChaUTp6U2MURADzDd999p9dee01fffWVunTpYjoOMokJJYzYsCEjZVKScslRJjPn0iVpzZpMvw0AYMCaNWvUuXNnde7cWW+99ZbpOMgCCiWMiIrK3jUj/fykLVuy7/wAANc4dOiQnn32WTVt2lQjRoxgeSAPRaGEETt2ZO/57fbs/wwAgHMuXbqkNm3aqGjRopo1axbLA3kwf9MB4JsuX5aSk7Pv/DabdPFi9p0fAOCcpKQkPf/88zp58qQ2b96swoULm44EJ1AoYURObJHoz/+7AcBt9ezZUytWrNDSpUtVuXJl03HgJC55w4jSpbN3i0SrNVl2+1GdOXMm+z4EAJAl48aN04gRIzRy5Ei1bNnSdBy4AIUSRgQHS4mJ2Xd+m82iZcs+VokSJVSuXDm1a9dOn332mdatW6crV65k3wcDANK0evVqvfXWW3rrrbf05ptvmo4DF2EdShixZ490332ZfVfG16GUpEWLjisuboMiIiIUGRmpLVu26OrVq7JarapWrZrq1aunkJAQ1atXTzVq1FBgYGCmfx8AgIw7cOCA6tevr+DgYC1ZskT+3JvkNSiUMCYkxLG0j82W3pGjJF2UdELSN5KekVT7z+91lVQwxdFWq1SjhrRtm/TX1SeSkpK0d+/eWwUzIiJCv/32m5KSkpQrVy7Vrl07RcmsVKmSrFaG+ADgChcvXlSDBg1kt9t5CMcLUShhzNSp0ksvZeTIeyQdSeV7sX9+P6Xx46VXX03/zNeuXdP27dtTlMwDBw5IkgoWLKi6desqJCTkVsm88847MxIYAPAXSUlJevzxxxUZGanw8HBVqlTJdCS4GIUSxiQnS02aOBY5T0pyzTn9/KT775c2b876U94XLlxQVFRUipJ58uRJSVLp0qVTTDHr1q3LT9kAkI5u3brpm2++0bJly9SiRQvTcZANKJQwKjpaqllTSkhwLEbuDIvFUSJ37JCqVnVNvpuOHz+eomBGRUXp0qVLkqRKlSqlmGLef//9ys0m4gAgSRozZow6d+6sb775Rm+88YbpOMgmFEoYt2iR9OSTNtlsdklZW6DSYnF8zZkj/etfLo13WzabTQcOHEhRMrdv364bN27I399fNWrUuFUwQ0JCVK1aNfnlxOKbAOBGVq1apVatWunNN9/UyJEjTcdBNqJQwrjt27erQYPBSkr6QRZLLiUlZW4fV39/KTBQmjFDatMmm0JmQEJCgn777bcUJXPPnj2y2+3Kmzev6tSpk6Jk3nPPPexZC8Br3Xyiu169elq0aBFPdHs5CiWMOnHihEJCQlSqVClNn75OXbvm0S+/OEpievdV3jzmoYek77+X7r47ZzJnRlxcnLZu3XqrYEZGRurw4cOSpGLFiqlevXop7sksUaKE2cAA4AIXLlxQgwYNZLFYtHnzZhUqVMh0JGQzCiWMiY+PV9OmTfXHH38oPDxcpUuXlt0urVkjjR4tzZvnWFLIav3/rRqTk///tSeflN56y1EoPWnQd/r0aUVGRqYomWfPnpUklS1bNsUUMzg4WPny5TOcGAAyLjExUY899pi2bNmiiIgIVaxY0XQk5AAKJYyw2Wx69tlntXz5cm3YsEH333//P46Ji3OsJbl1q3TunOOhnaJFpTp1pNq1pQIFcj53drDb7Tp8+PCtghkREXFrEXaLxaJq1aqlKJkswg7AnXXp0kVjx47VL7/8oubNm5uOgxxCoYQRffr00bBhwzR//ny1MXnjo5u6uQj7X6eYO3fuvLUI+/3333+rYIaEhLAIOwC38PXXX+utt97SmDFj9L///c90HOQgCiVy3HfffafXXntNX3zxhbp37246jse4du2aduzYcWuKGRkZqejoaElSgQIF/nE/5p133slDPwByzIoVK/TII4+oS5cu+vLLL03HQQ6jUCJHrVq1Sq1bt1anTp309ddfU3icdOHChVv3Kd2cZp44cUKSdMcdd6SYYrIIO4DsEh0drfr166t+/fpauHAhT3T7IAolcsy+ffvUsGFDhYSEaOHChQoICDAdySsdP348xaXyyMjIFIuw/3WKWbt2bRZhB+CUCxcuqH79+vL399emTZtUsGBB05FgAIUSOeLs2bNq0KCBcuXKpY0bN/IvnBxks9l08ODBFJfKt23blmIR9r+WzGrVqjFdAJAhiYmJevTRR7Vt2zZFRESoQoUKpiPBEAolst2NGzfUsmVL7d+/X+Hh4SpXrpzpSD4vISFBu3bt+sci7DabTXny5PnHIuzlypXj9gQA//Dmm2/q22+/1fLly9WsWTPTcWAQhRLZym63q0OHDvrxxx+1evVqNWzY0HQkpOLKlSvaunVripJ5cxH2okWLpphi1qtXTyVLljQbGIBRo0ePVpcuXfTtt9+qU6dOpuPAMAolstWHH36oAQMGaPr06XrhhRdMx0EmnTlzJsUi7BEREbcWYb/77rtvPfBTr149BQcHK3/+/IYTu8jly1JUlLRli/T7744tmfLnl2rUkIKDpSpVPGs1fcDFfvnlFz322GPq1q2bPv/8c9Nx4AYolMg2M2fO1L///W8NHjxYAwcONB0HLmC323XkyJEUU8wtW7YoPj5eFotFVatWTXGpvGbNmp61CHtEhPTVV46N4ZOSUm7TJEmJiY5fK1SQunWTOnb0nhX2gQzat2+fGjRooEaNGmnBggXy++s/I/BZFEpki82bN6tZs2Z67rnnNHnyZO6/82LJyckpFmGPiIi4tQh7YGCg7r///hQl895773W/RdgvXZJ69JAmTMjYRvI3//9cooTjPY8+mv0ZATdw/vx51a9fX4GBgTxgiRQolHC5w4cPq379+rr33nu1YsUK5cqVy3Qk5LDr169r+/btKZYv2r9/vyTHIux169ZNUTKNLsK+a5fUqpV0+rRjs/jMsFodm8u//bb0+eeOvwe8VGJiolq3bq2dO3cqIiJC5cuXNx0JboRCCZe6dOmSGjdurGvXrik8PFzFihUzHQlu4uLFi4qKikpRMo8fPy5JKlWqVIqCWbduXRUpUiT7Q+3ZIzVu7Ng4PrNl8u9ef10aM4Z7K+GV7Ha7OnfurO+//14rVqzQgw8+aDoS3AyFEi6TlJSkJ554Qps3b9bmzZtVpUoV05Hg5k6cOJHiUnlUVJQuXrwoSapYsWKKkunyRdjj46X77pOOHXO+TN709ddS586uORfgRr766it169ZN3333nf773/+ajgM3RKGES9jtdnXp0kXjxo3T0qVL9dBDD5mOBA90cxH2v04xt27dqhs3bsjPzy/FIuwhISHOLcLerZs0erTjkvXf7JY0SNIWSack5ZFUTVIvSW3SOmdQkGPqyVqr8CJLly7V448/rh49euizzz4zHQduikIJlxg5cqTefvttjRs3Tq+99prpOPAiiYmJ+u2331KUzN27d6dYhP2va2SWL18+/fsx9+93LP2TisWSRkpqKKm0pKuS5khaL2mspNdTe6O/v/Tss46nxAEvsHfvXjVo0EAPPPCA5s+fzxPdSBWFEk5btGiRnnzySb3zzjsaNmyY6TjwAVeuXLm11dvNohkbGytJKlKkSIpL5bddhL1HD2nUqPSf5v6LZEnBkq5L2pfWgf7+jrUrS5XK5O8KcC/nzp1T/fr1FRQUpI0bN6oAS2QhDRRKOGXHjh1q0qSJWrZsqdmzZ/PTK4w5c+aMoqKiUpTMM2fOSHIswn6rYNapo2bPPCNLXFymP6ONpEg5LoOnymqVhg6V3n03K78NwC0kJCSoVatW2r17tyIiItgyF+miUCLLTp48qZCQEJUoUULr1q1T3rx5TUcCbrHb7Tp69GiKghkVFaW74uO1N4PniJd0TdIlST/LcQ/l85KmpfUmPz/p6aelWbOcyg+YYrfb9b///U8TJ07UqlWr1KRJE9OR4AEolMiSq1evqmnTpjp58qTCw8N15513mo4EpCs5OVknP/tMZfr2zdDxb8hxz6QkWSU9I2mcpMLpvbFMGcdlb8ADjRgxQt27d9eECRPUsWNH03HgIbL4eCR8mc1m00svvaQ9e/Zow4YNlEl4DD8/P5Xx93dMETOwVFB3SW0lnZD0oxz3USZk5IP+3O8c8DRLlizRO++8o169elEmkSkUSmTa+++/r3nz5umnn35S7dq1TccBMuc2ywSlpsqfX5L0sqRWctxHGS4pzefIXbWuJZCD9uzZo3//+9967LHHNGTIENNx4GHYJwyZMmHCBH3yySf67LPP9OSTT5qOA2ReoUJZLnxt5XgoJzqd4+z582fp/IApZ8+eVZs2bXT33Xdr+vTpPGCJTGNCiQxbvXq1Xn/9df3vf/9Tjx49TMcBsqZWrSy/9dqfv15K4xibpJXnz6tPnTq3FmAPCQlR1apV+Y803FJCQoKeffZZxcXFaeXKlcrPD0TIAh7KQYZER0erQYMGqlu3rhYtWqSAgADTkYCsuX5dyp8/zTUoT0sq8bfXEiU1kLT3z+/nS+W9dj8/bX34YY2+4w5FRERoz549stvtyps3r4KDg1OskVm2bNn0F2EHspHdbtdrr72mKVOmaOXKlTzRjSyjUCJd586dU4MGDRQQEKCNGzeqUKFCpiMBzmnbVpo/P9VS+bSky5IelHSnHOtOTpNjQfPhkt5J7/w7d0o1akiS4uLitHXr1hTLFx05ckSSVLx48X8swl6sWDEX/AaBjPniiy/0zjvvaOLEierQoYPpOPBgFEqk6caNG2rVqpX27Nmj8PBwlS9f3nQkwHmrV0stWqT67RmSxkv6TdI5Sfnl2CWnq6Q07xy2WqX69aWNG9P8+D/++EORkZG3CmZERITOnz8vSSpXrlyKS+W1a9dmjVdki5u7nPXs2VOffvqp6TjwcBRKpMput+uVV17RjBkztGrVKjVq1Mh0JMA17HapeXPp118ztf1ihqxcmWZZvX0cu2JjY2+Vy4iICG3dulXXrl2T1WpV9erVU0wyq1evLn9/boFH1u3evVsNGzZU8+bNNXfuXO7vhdMolEjVxx9/rPfff1/Tpk3Tiy++aDoO4FqxsVK1atKNG46C6Sw/P+m116RvvnH+XJKSkpJubXt383L5b7/9JpvNpty5c6tOnTq3CmZISIjKly/P/ZjIkDNnzqh+/frKnz+/NmzYwEM4cAkKJW5r1qxZateunQYNGqQPPvjAdBwge8yaJT3/vPOF0s/P8fT42rVSvtQe13FefHy8tm3bluJ+zJiYGElSkSJFUhTMevXqqWTJktmWBZ4pISFBLVu21P79+xUREaGyZcuajgQvQaHEP4SHh6tZs2Z65plnNHXqVKYe8G5Tp0odOkgWS9bWp7RapTp1pGXLpCJFXJ8vHWfPnlVUVFSKy+VnzpyRJN19990pCmZwcDDTKB9mt9v13//+V9OmTdPq1au5jQkuRaFECkeOHFH9+vVVoUIFrVy5UkFBQaYjAdlv82bppZekmJiM76Tj5+c49t13pdBQKXfu7M2YQXa7XUePHk1xqTwqKkrx8fGyWCyqVq1aivsxa9SoocDAQNOxkQOGDx+unj17avLkyXrppZdMx4GXoVDilsuXL6tx48aKj49XeHi4ihcvbjoSkHOuXZNGjJC++ko6cULy93dMLP/6r8ibr0lSmzZSv36Op7rdXHJysvbu3ZviUvnOnTuVlJSkXLly6f7770/xZHnFihVltbKRmjdZuHChnnzySfXp04dtFZEtKJSQ5HgA4Mknn9TGjRu1ceNGVatWzXQkwIzkZGn5cscT4BER0uHDUmKiVLCgVLu2FBzsKJN33206qVOuXbum7du3p1i66MCBA5KkggULplgbMyQkRKVLlzacGFm1a9cuNWzYUC1bttScOXP4YQHZgkIJSVLXrl31zTffaOnSpWrZsqXpOAAMuHDhwj/uxzx16pQk6c4770xRMOvWrauCBQsaToz0nD59WvXr11fBggW1YcMG5cvGh8bg2yiU0FdffaVu3bpp7Nixev31103HAeAm7Ha7jh8/nuJSeWRkpOLi4iRJlStXTnGpvFatWsqVK5fh1Ljpxo0beuihh3Tw4EFFRETobg+fqsO9USh93OLFi9WmTRt1795dw4cPNx0HgJuz2Wzav39/ikvlO3bsUEJCggICAlSrVq0UT5ZXqVKFS6wG2O12vfrqq/rhhx+0evVqNWzY0HQkeDkKpQ/buXOnGjdurBYtWrBTAoAsu3Hjhnbu3JniyfK9e/dKkvLnz6+6deumWCOzTJkyLEeWzYYNG6bevXtr6tSpat++vek48AEUSh916tQphYSEqGjRolq/fj331QBwqUuXLmnLli0pLpcfO3ZMklSqVKkUBbNu3boqYmANT2/1888/61//+pfee+89ffTRR6bjwEdQKH3Q1atX1axZMx0/flzh4eEqU6aM6UgAfMCJEycUGRmZ4n7MixcvSpIqVqyY4lJ57dq1ldtN1vb0JDevPD388MOaPXs2txsgx1AofYzNZtPzzz+vxYsXa/369apTp47pSAB8lM1m06FDh1I8Vb5t2zbduHFD/v7+qlGjRopJZrVq1bg1Jw1//PGHQkJCVKRIEW3YsEF58+Y1HQk+hELpY/r166dPPvlEc+fO1b/+9S/TcQAghYSEBO3atSvFpfLdu3fLbrcrb968qlOnToony8uWLeu192Pa7VJCgmNDply5HLt8pubGjRtq0aKFDh06pMjISN111105FxQQhdKnTJw4Ua+88oqGDRumnj17mo4DABkSFxenrVu3pniy/MiRI5KkYsWKpSiY9erVU7FixQwnzrroaGnSJMe6+lu3Sn+u0KSAAKlGDalBA+nf/5aaNHFsPy85nuju2LGjZs6cqbVr16q+B+zeBO9DofQRa9eu1cMPP6yOHTtq7NixXvsTPQDfcPr06RQFMzIyUufOnZMklStXLsUi7HXq1HH7y787dkg9ekirVzu2ib+5w+ff+ftLSUlSlSrSJ59ITz0lffrpp+rbt6+mTZumF198MWeDA3+iUPqA6OhoNWjQQHXq1NGSJUsUEBBgOhIAuJTdbldsbGyKS+VbtmzRtWvXZLVaVb169RT3Y953331u8e/C5GTpo4+k0ND///uMsFgcl8SbNDmmDRtqqn//txQWFpZ9QYF0UCi93Pnz59WgQQP5+flp48aNKly4sOlIAJAjkpKStHv37hSTzF27dik5OVlBQUEp7sesV6+eKlSokKNXbxITpRdekObOdZTDrElS/vyntH9/ad1xB090wxwKpRdLSEhQq1attGvXLoWHh6tChQqmIwGAUVevXtW2bdtSXCo/dOiQJKlIkSKqV69eiklmyZIlsyWH3S516CBNnepMmXTw87OrcmWLwsMllhSGKRRKL3Vz263p06dr5cqVatKkielIAOCWzp07l2JtzIiICJ0+fVqSdPfdd6comMHBwcqfP7/Tn/nDD5Irb3e0WqXOnaVRo1x3TiAzKJRe6pNPPtF7773HtlsAkEl2u11Hjx5Ncak8KipK8fHxslgsqlq1aopL5TVr1lRgYGCGz3/2rFSxonT5cmamkx9J6i/pPkm7Uj1q/XrHE+BATqNQeqHZs2frueee08CBAzV48GDTcQDA4yUnJ2vfvn0pFmHfuXOnkpKSFBgYqNq1a6d4srxSpUqp7lLzySfS++871pfMmGOSKkuySLpHqRVKPz+pdWtp0aJM//YAp1EovUxERISaNm2qf/3rX5o+fTrLAwFANrl+/bq2b9+e4n7M6OhoSVLBggVVt27dFGtkli5dWsnJUtmy0vHjmfmkf0s6IylZ0lmlNaG0WKRDh6Ry5bL++wKygkLpRY4ePaqQkBCVL19eq1atUlBQkOlIAOBTLly4oKioqFuXy8PDw3Xq1ClJUunSpXXvve20Zs0XmTjjOkktJG2T1FUZKZRffSW99VbWfw9AVvibDgDXuHz5sp544gnlzp1bP/30E2USAAwoXLiwHn74YT388MOSHPdjHj9+/FbB/OmnopLscly+Tk+yHCWyk6QaGfp8Pz9py5asZQecQaH0AklJSXrhhRd05MgRbdy4USVKlDAdCQAgyWKxqEyZMipTpoyefvppXb8uHTpkV2JiRt49RtIRSSsy/HlJSY5dd4CcRqH0Au+++66WLVumxYsX67777jMdBwCQiqtXJbs9I9PJc5IGShogqXimPuPm/t9ATqJQerjRo0dr5MiR+vrrr9WqVSvTcQAAafD3d9znmL7+korIcck7c9xgR0n4IAqlB1u6dKm6deum7t27q3PnzqbjAADScc89Gdmv+4CkcZK+lHTiL69fl5Qo6bCkAnIUzpSsVscal0BOY+NPD7Vr1y61a9dOjz32mD777DPTcQAAGRAcnJH1J49LsknqJqncX77CJUX/+deht32nxSLVreuqtEDGsWyQBzp16pTq16+vwoULa8OGDcrH5q0A4BEuX5aKF5cSEtI66qykDbd5vb+kOEkjJFVQak9+r1kjNW3qXE4gsyiUHubatWtq3ry5jh49qvDwcN11112mIwEAMuGVV6SpUx1PZGdOM6W1DqXFIpUvLx04kNH7NAHX4ZK3B7HZbOrQoYN27typBQsWUCYBwAN17ZqVMpkx3btTJmEGhdKDDBw4ULNnz9a0adMUHBxsOg4AIAvq1JE6d3Y8QJM5a5TadNLfX6pZU3rjDSfDAVnEJW8PMXnyZHXo0EGffvqpevfubToOAMAJV65I1as79vR2dlppsTiWCtqyxXFOwAQKpQdYt26dWrZsqZdfflnffvutLFzPAACPd/Cg1KiRdOFC1kulxeLYbvGnn6THH3dpPCBTKJRu7uDBg6pfv75q1aqlpUuXKjAw0HQkAICLxMRITzwh7dsnZfa/xn5+dhUoYNHMmdKfW4cDxlAo3dj58+fVsGFDWSwWbdq0SYULFzYdCQDgYgkJUliYNGSI4+/TW/jcz8+u5GSLataM1ooV96p45nZmBLIFD+W4qYSEBLVt21Znz57VwoULKZMA4KUCAx2F8uhRaeBAqUyZ1I8tUEB6/XWLnnpqgE6dekB58sTnXFAgDUwo3ZDdblenTp00ZcoUrVy5Ug888IDpSACAHPTHH46HbP74w7GzTqFCUu3aUrlyjvsmY2Njde+99+qjjz7iQU24BQqlGxo6dKj69OmjSZMm6eWXXzYdBwDght544w3Nnj1bsbGxyp8/v+k48HFc8nYzc+fOVZ8+fdS/f3/KJAAgVe+//77i4uI0YsQI01EAJpTuJCoqSg8++KDatGmjH374QdbMr3oLAPAh3bp105QpUxQbG6tChQqZjgMfRqF0E7///rtCQkJUtmxZrV69Wrlz5zYdCQDg5k6ePKny5curV69eCg0NNR0HPoxC6Qbi4uL0wAMP6OLFiwoPD1fJkiVNRwIAeIiePXtq3Lhxio2NVdGiRU3HgY/imqphycnJeuGFFxQTE6OFCxdSJgEAmdKnTx/ZbDYNGzbMdBT4MAqlYT179tSSJUv0448/qjqbsAIAMql48eLq1q2bvvrqK/3xxx+m48BHUSgN+uabb/Tll1/qq6++0iOPPGI6DgDAQ/Xs2VP+/v769NNPTUeBj6JQGrJs2TJ17dpV3bp105tvvmk6DgDAgxUpUkQ9evTQN998oxMnTpiOAx/EQzkG7N69W40aNdIDDzyg+fPny8/Pz3QkAICHu3TpksqVK6cXX3xRo0aNMh0HPoZCmcP++OMP1a9fXwULFtSGDRvY3QAA4DIff/yxBg8erAMHDujuu+82HQc+hEKZg65du6YWLVro8OHDCg8P5x92AIBLXblyReXKldPTTz+tcePGmY4DH8I9lDnEZrPplVde0Y4dO/Tzzz9TJgEALpcvXz716dNHEyZMUExMjOk48CEUyhwyaNAgzZw5U1OmTFG9evVMxwEAeKk333xTxYoVY+cc5CgKZQ6YOnWqwsLCNGTIED377LOm4wAAvFiePHnUr18/TZkyRfv37zcdBz6Ceyiz2YYNG/TQQw+pffv2Gj9+vCwWi+lIAAAvd/36dVWqVEkPPPCApk+fbjoOfACFMhsdOnRI9evXV40aNbRs2TIFBgaajgQA8BFjx45V586dtXPnTnZiQ7ajUGaTCxcuqGHDhrLZbNq8ebOKFCliOhIAwIckJCSocuXKqlOnjubMmWM6Drwc91Bmg8TERLVt21ZnzpzRokWLKJMAgBwXGBiogQMHau7cudq2bZvpOPByTChdzG636/XXX9ekSZO0fPlyNW3a1HQkAICPSkpKUrVq1VS5cmUtWLDAdBx4MSaULjZ8+HB99913+vbbbymTAACj/P399cEHH2jhwoUKDw83HQdejAmlC/3000965pln9N577+mjjz4yHQcAACUnJ6tmzZoqU6aMli1bZjoOvBSF0kW2bNmiBx98UI899phmzpwpq5XhLwDAPcyaNUvt2rXT+vXr1aRJE9Nx4IUolC5w7NgxhYSE6K677tKaNWuUO3du05EAALjFZrOpdu3aKlKkiFavXm06DrwQYzQnXblyRW3atFFAQIDmz59PmQQAuB2r1arQ0FCtWbNGq1atMh0HXogJpROSk5P19NNPa82aNfr1119Vo0YN05EAALgtu92ukJAQBQYGasOGDezcBpdiQumE3r17a9GiRZo5cyZlEgDg1iwWi0JDQ7Vx40YezoHLMaHMorFjx+qNN97QV199pS5dupiOAwBAuux2uxo3bqzExERFREQwpYTLMKHMguXLl+utt95Sly5dKJMAAI9hsVgUFhamqKgoFjqHSzGhzKQ9e/aoYcOGaty4sX7++Wf5+/ubjgQAQIbZ7XY1b95cFy9e1NatW1nmDi5BocyE06dPq0GDBsqbN69+/fVXFShQwHQkAAAybf369XrwwQc1a9YstW3b1nQceAHfLJRHj0orVkhbtkh790rx8VJQkFSlilS3rtS8uVSxYoq3XL9+XS1atFBMTIzCw8NVtmxZQ+EBAHBeq1atdPz4ce3cuVN+fn6m48DD+VahXLNGGjZMWrJEstulgAApMfH/v+/vLyUlOf66RQupZ0/p0Udlt9vVvn17zZs3T2vXrlVISIiR+AAAuEp4eLgaNGigadOm6cUXXzQdBx7ONwrlpUvSu+9K48dLfn5ScnL677l5XLt2Glq2rPoMG6Yff/xRzz33XPbnBQAgBzzxxBOKjo7Wnj17eCYATvH+Qnn4sOMS9u+/Z6xI/o3NatVpm03z335b//vyS5fHAwDAlK1btyo4OFgTJkxQx44dTceBB/PuQnnihFS/vnTq1P9fys6CZItF1iJFZNm8+R/3VgIA4MmeeeYZbd++Xfv371dAQIDpOPBQ3rtWgM0mvfCC02VSkvzsdlkuXpTatk15zyUAAB5u8ODBOnz4sCZMmGA6CjyY9xbKsWOldetuWyYjJXWRdJ+kvJLultROUnRa50tOlnbulIYOzYawAACYUaNGDbVr104ffvihbty4YToOPJR3XvK+cUO64w7pwoXbfrutpF8lPSeppqRTkkZJuiJps6TqaZ07KMgx9SxY0KWRAQAwZd++fbrvvvs0YsQIdoBDlnhnoZw+XWrfPtVvb5RUV1LgX147IKmGHGVzalrntlikkSMl/oEDAHiRl19+WStWrNChQ4eUO3du03HgYbzzkveUKVIaW0k1UsoyKUmV5LgEvjcj5580KcvRAABwRwMHDtTp06f1zTffmI4CD+R9E0q7XSpaNNXL3am+TdJdcpTKZekdHBDg2F2Hp+EAAF7ktdde0/z58xUTE6N8+fKZjgMP4n0TypMnM10mJWmapOOSns/IwYmJ0r59mf4MAADcWf/+/XXx4kWNGjXKdBR4GO8rlOfOZfot+yS9JamhpA4ZfdP585n+HAAA3FnZsmX12muvaejQobp06ZLpOPAg3lcoLZZMHX5K0uOSCkqaLckvmz4HAABP0K9fP129elVfsjscMsH7CmWJEhk+9JKkRyVdlLRUUunMfE7x4pk5GgAAj3DnnXeqc+fO+vzzz3Weq3HIIO8slBkoe9cltZFjMfOFkqpl5jOCgqR7781SPAAA3F3fvn2VlJSk4cOHm44CD+F9hVKSGjeW/FK/eJ0sx8M3myTNkuPeyQyzWqXg4DTPDwCAJytZsqS6dOmiESNG6MyZM6bjwAN4Z6Hs2NGxVWIq3pX0sxyXu8/LsZD5X7/SZLNJr77qkpgAALirXr16yWKxaChbDiMDvG8dSsmxf/fddzu2SLzNb6+ZpLVpvD3NP5D8+R3nzZPHuYwAALi5AQMGaPjw4YqJiVGpUqVMx4Eb884Jpb+/9Pnnty2TkrRGjtKY2leaPvmEMgkA8AnvvPOOAgMDNWTIENNR4Oa8s1BK0vPPS08/7bp7Hf39pQcflN54wzXnAwDAzRUuXFjvvvuuxowZo2PHjpmOAzfmnZe8b7pwQWrSRIqOdlwGzyp/f+nOO6XNmyVG/gAAH3L58mWVK1dO7dq1Y59vpMp7J5SSVLiwtHatVLNm1hcit1qlChWkX3+lTAIAfE6BAgXUu3dvjR8/XocPHzYdB27KuwulJBUrJm3aJA0Y4Lj87e+fsff5+ztKaPfu0tatjgklAAA+qEuXLipcuLDCwsJMR4Gb8v5CKUmBgdLgwdLOnVKnTo6FySVHwfTzc0wh/1o2AwOl//xH2rJFGj6ch3AAAD4tb9686tu3ryZNmqSDBw+ajgM35N33UKbm8mXH1HLLFmnfPun6dUeJvPdeqW5dqWFDx+VyAAAgSbp27ZoqVqyoFi1aaMqUKabjwM34ZqEEAACZNnr0aHXt2lW7d+9W1apVTceBG6FQAgCADLlx44YqVaqkhg0baubMmabjwI34xj2UAADAably5dKAAQP0448/aufOnabjwI0woQQAABmWmJioKlWqqGbNmpo3b57pOHATTCgBAECGBQQEaODAgfrpp5+0ZcsW03HgJphQAgCATElKStJ9992nihUratGiRabjwA0woQQAAJni7++vQYMGafHixdq0aZPpOHADTCgBAECm2Ww21axZU3fccYeWL19uOg4MY0IJAAAyzWq1avDgwVqxYoXWrVtnOg4MY0IJAACyxGazKTg4WAUKFNCaNWtksVhMR4IhTCgBAECWWK1WhYaGat26dVq5cqXpODCICSUAAMgyu92uBg0ayGq1auPGjUwpfRQTSgAAkGUWi0VhYWHavHmzlixZYjoODGFCCQAAnGK32/Xggw/q2rVrioyMZErpg5hQAgAAp9ycUm7ZskXz5883HQcGMKEEAAAu8dBDD+n06dPasWOHrFZmVr6E/7UBAIBLhIWFadeuXZo1a5bpKMhhTCgBAIDLPProozp8+LB27dolPz8/03GQQ5hQAgAAlwkNDdW+ffs0ffp001GQg5hQAgAAl3rqqae0e/du7d27VwEBAabjIAcwoQQAAC4VGhqqQ4cOafLkyaajIIcwoQQAAC733HPPKTIyUtHR0QoMDDQdB9mMCSUAAHC5QYMG6ejRoxo/frzpKMgBTCgBAEC2aN++vdauXauDBw8qKCjIdBxkIyaUAAAgW3zwwQc6efKkxo4dazoKshkTSgAAkG1eeeUVLVmyRDExMcqTJ4/pOMgmTCgBAEC2GThwoM6dO6fRo0ebjoJsxIQSAABkq//973+aM2eOYmNjlT9/ftNxkA2YUAIAgGzVv39/xcXFaeTIkaajIJswoQQAANmua9eumjp1qmJjY1WoUCHTceBiTCgBAEC269evn65fv64vvvjCdBRkAwolAADIdnfccYfefPNNffHFFzp37pzpOHAxCiUAAMgRffr0kc1m02effWY6ClyMQgkAAHJEiRIl1LVrV40cOVKnT582HQcuRKEEAAA5pmfPnvLz89Onn35qOgpciEIJAAByTNGiRdWjRw99/fXXOnHihOk4cBEKJQAAyFE9evRQUFCQhgwZYjoKXIRCCQAAclShQoXUs2dPjRs3TkePHjUdBy7AwuYAACDHxcXFqVy5cnr22Wc1duxY03HgJCaUAAAgx+XPn199+/bV999/r5iYGNNx4CQmlAAAwIirV6+qQoUKeuSRRzRhwgTTceAEJpQAAMCIPHny6L333tPkyZMVHR1tOg6cwIQSAAAYc/36dVWqVEkPPPCApk+fbjoOsogJJQAAMCYoKEjvv/++ZsyYoV27dpmOgyxiQgkAAIxKSEhQ5cqVFRwcrNmzZ5uOgyxgQgkAAIwKDAzUgAEDNGfOHG3fvt10HGQBE0oAAGBcUlKSqlatqqpVq+rnn382HQeZxIQSAAAY5+/vrw8++EALFixQRESE6TjIJCaUAADALSQnJ6tGjRq6++67tXTpUtNxkAlMKAEAgFvw8/PToEGDtGzZMv3666+m4yATmFACAAC3YbPZVLt2bRUtWlSrVq0yHQcZxIQSAAC4DavVqsGDB2v16tVavXq16TjIICaUAADArdjtdtWrV09BQUFav369LBaL6UhIBxNKAADgViwWi0JDQ/Xrr7/ql19+MR0HGcCEEgAAuB273a5GjRopOTlZ4eHhTCndHBNKAADgdiwWi8LCwhQZGamFCxeajoN0MKEEAABuyW63q1mzZrp8+bK2bNkiq5U5mLvifxkAAOCWbk4pt2/frnnz5pmOgzQwoQQAAG7t4Ycf1smTJ7Vjxw75+fmZjoPbYEIJAADcWlhYmHbv3q0ff/zRdBSkggklAABwe48//rgOHjyo3bt3y9/f33Qc/A0TSgAA4PZCQ0MVHR2tadOmmY6C22BCCQAAPMLTTz+tnTt3at++fQoICDAdB3/BhBIAAHiEwYMHKyYmRhMnTjQdBX/DhBIAAHiM559/Xps2bdKBAweUK1cu03HwJyaUAADAYwwaNEjHjx/Xd999ZzoK/oIJJQAA8Cgvv/yyVqxYoUOHDil37tym40BMKAEAgIcZOHCgTp8+rTFjxpiOgj8xoQQAAB6nU6dOWrBggWJiYpQ3b17TcXweE0oAAOBxBgwYoAsXLmjUqFGmo0BMKAEAgId68803NXPmTMXGxqpAgQKm4/g0JpQAAMAjvf/++4qPj9eXX35pOorPY0IJAAA8Vvfu3TVx4kTFxsaqcOHCpuP4LCaUAADAY/Xt21cJCQkaPny46Sg+jUIJAAA8VqlSpdSlSxeNGDFCZ8+eNR3HZ1EoAQCAR+vdu7ckaejQoYaT+C4KJQAA8GjFihXT22+/rVGjRunUqVOm4/gkCiUAAPB47777rgIDA/XJJ5+YjuKTKJQAAMDjFS5cWO+8847GjBmjY8eOmY7jc1g2CAAAeIXLly+rXLlyev755/X111+bjuNTmFACAACvUKBAAfXq1Uvfffedjhw5YjqOT2FCCQAAvMaVK1dUvnx5Pfnkk/ruu+8cL16/Lu3cKR06JCUkSLlzS9WqSVWqSP7+ZgN7Cf4UAQCA18iXL5/69u2r/r166cNq1VRqzhwpPFxKTv7nwblySa1aSV26SC1bSlYu3GYVE0oAAOBVbsyercvPP6/iNpujJNpsqR/s7y8lJUnVq0tTpkj3359jOb0JVRwAAHiHGzekV15RrueeU9Gb87K0yqTkKJOStHevVLeu9OmnErO2TGNCCQAAPF9CgvTUU9Ivv6RfItPTp480ZIhksbgmmw9gQgkAADzfW2+5pkxKjinl2LHOn8eHUCgBAIBnW7pU+u67NMvkVklPSioiKY+k6pJGpnXOHj2k2FhXpvRqXPIGAACeKylJuuce6eTJVAvlL5LaSKot6XlJ+SQdkmSTNDS18/r7S61bSwsXujyyN6JQAgAAzzV3rvTss6l++7KkeyU1kjRbmbw0a7FIBw9K5cs7FdEXcMkbAAB4rq+/lvz8Uv32dEl/SPpIjtITL8dkMkOsVseldKSLQgkAADxTcrL066+3X7T8TyskFZB0XFJlOS53F5DUWdL1jJx/5UrXZPVyFEoAAOCZ9u93bKuYhgOSkiQ9Jam1pDmSXpU0RtIrGfmMnTvTLKxwYOtFAADgmTLwFPYVSVclvaH/f6r7GUkJksZKCpVUKa0TXL8unT4t3XGHU1G9HRNKAADgmRIT0z0k95+/vvC311/889dNLvocX0ehBAAAnilv3nQPKf3nryX/9nqJP3+9kJHPyZMn45l8FIUSAAB4pmrV0j0k+M9fj//t9RN//lo8vRMULer4QpoolAAAwDOVLp1u2Wv356/j//b6d3I8SNIsrTdbLFK9euzpnQEUSgAA4JksFumppxy72qSithxPdU+XY5ecr+UomT9I6qX/vySeqjZtXBLV27FTDgAA8Fxbt0rBwWkekijpY0kT5LjUXVbSW5K6p3fu3LmlP/6Q8ud3PqeXo1ACAADP9tBD0rp1jn29XcVqlXr1kj75xHXn9GIUSgAA4NkOH3Y8oHPtmmvO5+cn3XOP9Ntvjikl0sU9lAAAwLPdc480ZoxrzmW1Ou7J/OEHymQmUCgBAIDne/llaeSfe+Fk9alsPz8pMFBasMDxdDcyjEIJAAC8Q9eu0ty5UqFCjnKYGRaLVKGCtGGD9PDD2RLPm1EoAQCA93j6aWn/fsfEMiDAcQk7tYnlzdJZoIDUv7+0Y0e6T4zj9ngoBwAAeKezZ6VJk6RVq6SICMff33TXXVKDBtKjj0rPP8/2ik6iUAIAAN9w9aqUkCAFBTm+4DIUSgAAADiFeygBAADgFAolAAAAnEKhBAAAgFMolAAAAHAKhRIAAABOoVACAADAKRRKAAAAOIVCCQAAAKdQKAEAAOAUCiUAAACcQqEEAACAUyiUAAAAcAqFEgAAAE6hUAIAAMApFEoAAAA4hUIJAAAAp1AoAQAA4BQKJQAAAJxCoQQAAIBTKJQAAABwCoUSAAAATqFQAgAAwCkUSgAAADiFQgkAAACnUCgBAADgFAolAAAAnEKhBAAAgFMolAAAAHAKhRIAAABOoVACAADAKRRKAAAAOIVCCQAAAKdQKAEAAOAUCiUAAACcQqEEAACAUyiUAAAAcAqFEgAAAE75P5Zpj07RwmWUAAAAAElFTkSuQmCC",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "G = nx.Graph()\n",
     "G.add_edges_from(max_cut_graph_edges)\n",

From 18790095e3500a175f639190c835ea854f3a88ad Mon Sep 17 00:00:00 2001
From: CalMacCQ <93673602+CalMacCQ@users.noreply.github.com>
Date: Tue, 24 Dec 2024 10:22:09 +0000
Subject: [PATCH 15/17] yet more cleanup

---
 .../pytket_qaoa_maxcut_example.ipynb          | 270 ++++++++++++++++--
 1 file changed, 254 insertions(+), 16 deletions(-)

diff --git a/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb b/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb
index 14e15297..7262c314 100644
--- a/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb
+++ b/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb
@@ -9,7 +9,9 @@
     }
    },
    "source": [
-    "# Quantum approximate optimisation algorithm (QAOA) applied to maxcut."
+    "# Solving Maxcut with QAOA\n",
+    "\n",
+    "**Download this notebook - {nb-download}`pytket_qaoa_maxcut_example.ipynb`**"
    ]
   },
   {
@@ -26,14 +28,25 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 1,
    "id": "9456fbeb",
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
     }
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "image/png": "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",
+      "text/plain": [
+       "<Figure size 200x200 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "import networkx as nx\n",
     "import matplotlib.pyplot as plt\n",
@@ -81,7 +94,7 @@
     "where\n",
     "\n",
     "$$\n",
-    "U( \\beta_i ) = e^{i \\beta H_B} \\quad \\& \\quad U ( \\gamma_i) = e^{i \\gamma H_P}\n",
+    "U( \\beta_i ) = e^{i \\beta_i H_B} \\quad \\& \\quad U ( \\gamma_i) = e^{i \\gamma_i H_P}\n",
     "$$\n",
     "\n",
     "with $H_P$ depending on the problem instance. "
@@ -206,14 +219,25 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 3,
    "id": "688f1332",
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
     }
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "import networkx as nx\n",
     "\n",
@@ -307,14 +331,93 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 4,
    "id": "0a9db628",
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
     }
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "\n",
+       "\n",
+       "\n",
+       "\n",
+       "\n",
+       "\n",
+       "<div style=\"resize: vertical; overflow: auto; height: 300px; display: block\">\n",
+       "    <iframe srcdoc=\"\n",
+       "&lt;!DOCTYPE html&gt;\n",
+       "&lt;html lang=&#34;en&#34;&gt;\n",
+       "&lt;head&gt;\n",
+       "    &lt;meta charset=&#34;UTF-8&#34;&gt;\n",
+       "    &lt;!-- Download Vue 3--&gt;\n",
+       "&lt;script type=&#34;application/javascript&#34; src=&#34;https://cdn.jsdelivr.net/npm/vue@3&#34;&gt;&lt;/script&gt;\n",
+       "&lt;!-- Download Circuit Renderer with styles --&gt;\n",
+       "&lt;script type=&#34;application/javascript&#34; src=&#34;https://unpkg.com/pytket-circuit-renderer@0.10/dist/pytket-circuit-renderer.umd.js&#34;&gt;&lt;/script&gt;\n",
+       "&lt;link rel=&#34;stylesheet&#34; href=&#34;https://unpkg.com/pytket-circuit-renderer@0.10/dist/pytket-circuit-renderer.css&#34;&gt;\n",
+       "&lt;/head&gt;\n",
+       "&lt;body&gt;\n",
+       "\n",
+       "\n",
+       "    &lt;div id=&#34;circuit-display-vue-container-35911ebf-49d7-4448-b48a-c0b4c8a3cc5a&#34; class=&#34;pytket-circuit-display-container&#34;&gt;\n",
+       "        &lt;div style=&#34;display: none&#34;&gt;\n",
+       "            &lt;div id=&#34;circuit-json-to-display&#34;&gt;{&#34;bits&#34;: [], &#34;commands&#34;: [{&#34;args&#34;: [[&#34;q&#34;, [0]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [1]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [2]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [3]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [4]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [5]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [6]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}], &#34;created_qubits&#34;: [], &#34;discarded_qubits&#34;: [], &#34;implicit_permutation&#34;: [[[&#34;q&#34;, [0]], [&#34;q&#34;, [0]]], [[&#34;q&#34;, [1]], [&#34;q&#34;, [1]]], [[&#34;q&#34;, [2]], [&#34;q&#34;, [2]]], [[&#34;q&#34;, [3]], [&#34;q&#34;, [3]]], [[&#34;q&#34;, [4]], [&#34;q&#34;, [4]]], [[&#34;q&#34;, [5]], [&#34;q&#34;, [5]]], [[&#34;q&#34;, [6]], [&#34;q&#34;, [6]]]], &#34;phase&#34;: &#34;0.0&#34;, &#34;qubits&#34;: [[&#34;q&#34;, [0]], [&#34;q&#34;, [1]], [&#34;q&#34;, [2]], [&#34;q&#34;, [3]], [&#34;q&#34;, [4]], [&#34;q&#34;, [5]], [&#34;q&#34;, [6]]]}&lt;/div&gt;\n",
+       "        &lt;/div&gt;\n",
+       "        &lt;circuit-display-container\n",
+       "                :circuit-element-str=&#34;&#39;#circuit-json-to-display&#39;&#34;\n",
+       "                :init-render-options=&#34;initRenderOptions&#34;\n",
+       "                view-format=&#34;None&#34;\n",
+       "        &gt;&lt;/circuit-display-container&gt;\n",
+       "    &lt;/div&gt;\n",
+       "    &lt;script type=&#34;application/javascript&#34;&gt;\n",
+       "      const circuitRendererUid = &#34;35911ebf-49d7-4448-b48a-c0b4c8a3cc5a&#34;;\n",
+       "      const displayOptions = JSON.parse(&#39;{&#34;zxStyle&#34;: true, &#34;condenseCBits&#34;: false}&#39;);\n",
+       "\n",
+       "      // Script to initialise the circuit renderer app\n",
+       "\n",
+       "const { createApp } = Vue;\n",
+       "const circuitDisplayContainer = window[&#34;pytket-circuit-renderer&#34;].default;\n",
+       "// Init variables to be shared between circuit display instances\n",
+       "if (typeof window.pytketCircuitDisplays === &#34;undefined&#34;) {\n",
+       "    window.pytketCircuitDisplays = {};\n",
+       "}\n",
+       "// Create the root Vue component\n",
+       "const app = createApp({\n",
+       "    delimiters: [&#39;[[#&#39;, &#39;#]]&#39;],\n",
+       "    components: { circuitDisplayContainer },\n",
+       "    data () {\n",
+       "      return {\n",
+       "        initRenderOptions: displayOptions,\n",
+       "      }\n",
+       "    }\n",
+       "})\n",
+       "app.config.unwrapInjectedRef = true;\n",
+       "app.mount(&#34;#circuit-display-vue-container-&#34;+circuitRendererUid);\n",
+       "window.pytketCircuitDisplays[circuitRendererUid] = app;\n",
+       "    &lt;/script&gt;\n",
+       "\n",
+       "\n",
+       "\n",
+       "&lt;/body&gt;\n",
+       "&lt;/html&gt;\n",
+       "\"\n",
+       "            width=\"100%\" height=\"100%\"\n",
+       "            style=\"border: none; outline: none; overflow: auto\"></iframe>\n",
+       "</div>\n",
+       "\n"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "from pytket import Circuit\n",
     "from pytket.circuit.display import render_circuit_jupyter as draw\n",
@@ -420,10 +523,89 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 8,
    "id": "f97de321",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "\n",
+       "\n",
+       "\n",
+       "\n",
+       "\n",
+       "\n",
+       "<div style=\"resize: vertical; overflow: auto; height: 300px; display: block\">\n",
+       "    <iframe srcdoc=\"\n",
+       "&lt;!DOCTYPE html&gt;\n",
+       "&lt;html lang=&#34;en&#34;&gt;\n",
+       "&lt;head&gt;\n",
+       "    &lt;meta charset=&#34;UTF-8&#34;&gt;\n",
+       "    &lt;!-- Download Vue 3--&gt;\n",
+       "&lt;script type=&#34;application/javascript&#34; src=&#34;https://cdn.jsdelivr.net/npm/vue@3&#34;&gt;&lt;/script&gt;\n",
+       "&lt;!-- Download Circuit Renderer with styles --&gt;\n",
+       "&lt;script type=&#34;application/javascript&#34; src=&#34;https://unpkg.com/pytket-circuit-renderer@0.10/dist/pytket-circuit-renderer.umd.js&#34;&gt;&lt;/script&gt;\n",
+       "&lt;link rel=&#34;stylesheet&#34; href=&#34;https://unpkg.com/pytket-circuit-renderer@0.10/dist/pytket-circuit-renderer.css&#34;&gt;\n",
+       "&lt;/head&gt;\n",
+       "&lt;body&gt;\n",
+       "\n",
+       "\n",
+       "    &lt;div id=&#34;circuit-display-vue-container-937d5171-df4e-4a09-b230-f802a7dc94a2&#34; class=&#34;pytket-circuit-display-container&#34;&gt;\n",
+       "        &lt;div style=&#34;display: none&#34;&gt;\n",
+       "            &lt;div id=&#34;circuit-json-to-display&#34;&gt;{&#34;bits&#34;: [[&#34;c&#34;, [0]], [&#34;c&#34;, [1]], [&#34;c&#34;, [2]]], &#34;commands&#34;: [{&#34;args&#34;: [[&#34;q&#34;, [0]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [1]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [2]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [0]], [&#34;q&#34;, [1]]], &#34;op&#34;: {&#34;params&#34;: [&#34;-0.375&#34;], &#34;type&#34;: &#34;ZZPhase&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [1]], [&#34;q&#34;, [2]]], &#34;op&#34;: {&#34;params&#34;: [&#34;-0.375&#34;], &#34;type&#34;: &#34;ZZPhase&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [0]], [&#34;q&#34;, [1]], [&#34;q&#34;, [2]]], &#34;op&#34;: {&#34;data&#34;: &#34;&#34;, &#34;signature&#34;: [&#34;Q&#34;, &#34;Q&#34;, &#34;Q&#34;], &#34;type&#34;: &#34;Barrier&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [0]]], &#34;op&#34;: {&#34;params&#34;: [&#34;0.8&#34;], &#34;type&#34;: &#34;Rx&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [1]]], &#34;op&#34;: {&#34;params&#34;: [&#34;0.8&#34;], &#34;type&#34;: &#34;Rx&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [2]]], &#34;op&#34;: {&#34;params&#34;: [&#34;0.8&#34;], &#34;type&#34;: &#34;Rx&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [0]], [&#34;q&#34;, [1]]], &#34;op&#34;: {&#34;params&#34;: [&#34;-0.3&#34;], &#34;type&#34;: &#34;ZZPhase&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [1]], [&#34;q&#34;, [2]]], &#34;op&#34;: {&#34;params&#34;: [&#34;-0.3&#34;], &#34;type&#34;: &#34;ZZPhase&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [0]], [&#34;q&#34;, [1]], [&#34;q&#34;, [2]]], &#34;op&#34;: {&#34;data&#34;: &#34;&#34;, &#34;signature&#34;: [&#34;Q&#34;, &#34;Q&#34;, &#34;Q&#34;], &#34;type&#34;: &#34;Barrier&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [0]]], &#34;op&#34;: {&#34;params&#34;: [&#34;0.1&#34;], &#34;type&#34;: &#34;Rx&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [1]]], &#34;op&#34;: {&#34;params&#34;: [&#34;0.1&#34;], &#34;type&#34;: &#34;Rx&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [2]]], &#34;op&#34;: {&#34;params&#34;: [&#34;0.1&#34;], &#34;type&#34;: &#34;Rx&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [0]], [&#34;c&#34;, [0]]], &#34;op&#34;: {&#34;type&#34;: &#34;Measure&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [1]], [&#34;c&#34;, [1]]], &#34;op&#34;: {&#34;type&#34;: &#34;Measure&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [2]], [&#34;c&#34;, [2]]], &#34;op&#34;: {&#34;type&#34;: &#34;Measure&#34;}}], &#34;created_qubits&#34;: [], &#34;discarded_qubits&#34;: [], &#34;implicit_permutation&#34;: [[[&#34;q&#34;, [0]], [&#34;q&#34;, [0]]], [[&#34;q&#34;, [1]], [&#34;q&#34;, [1]]], [[&#34;q&#34;, [2]], [&#34;q&#34;, [2]]]], &#34;phase&#34;: &#34;0.0&#34;, &#34;qubits&#34;: [[&#34;q&#34;, [0]], [&#34;q&#34;, [1]], [&#34;q&#34;, [2]]]}&lt;/div&gt;\n",
+       "        &lt;/div&gt;\n",
+       "        &lt;circuit-display-container\n",
+       "                :circuit-element-str=&#34;&#39;#circuit-json-to-display&#39;&#34;\n",
+       "                :init-render-options=&#34;initRenderOptions&#34;\n",
+       "                view-format=&#34;None&#34;\n",
+       "        &gt;&lt;/circuit-display-container&gt;\n",
+       "    &lt;/div&gt;\n",
+       "    &lt;script type=&#34;application/javascript&#34;&gt;\n",
+       "      const circuitRendererUid = &#34;937d5171-df4e-4a09-b230-f802a7dc94a2&#34;;\n",
+       "      const displayOptions = JSON.parse(&#39;{&#34;zxStyle&#34;: true, &#34;condenseCBits&#34;: false}&#39;);\n",
+       "\n",
+       "      // Script to initialise the circuit renderer app\n",
+       "\n",
+       "const { createApp } = Vue;\n",
+       "const circuitDisplayContainer = window[&#34;pytket-circuit-renderer&#34;].default;\n",
+       "// Init variables to be shared between circuit display instances\n",
+       "if (typeof window.pytketCircuitDisplays === &#34;undefined&#34;) {\n",
+       "    window.pytketCircuitDisplays = {};\n",
+       "}\n",
+       "// Create the root Vue component\n",
+       "const app = createApp({\n",
+       "    delimiters: [&#39;[[#&#39;, &#39;#]]&#39;],\n",
+       "    components: { circuitDisplayContainer },\n",
+       "    data () {\n",
+       "      return {\n",
+       "        initRenderOptions: displayOptions,\n",
+       "      }\n",
+       "    }\n",
+       "})\n",
+       "app.config.unwrapInjectedRef = true;\n",
+       "app.mount(&#34;#circuit-display-vue-container-&#34;+circuitRendererUid);\n",
+       "window.pytketCircuitDisplays[circuitRendererUid] = app;\n",
+       "    &lt;/script&gt;\n",
+       "\n",
+       "\n",
+       "\n",
+       "&lt;/body&gt;\n",
+       "&lt;/html&gt;\n",
+       "\"\n",
+       "            width=\"100%\" height=\"100%\"\n",
+       "            style=\"border: none; outline: none; overflow: auto\"></iframe>\n",
+       "</div>\n",
+       "\n"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "from networkx import path_graph\n",
     "\n",
@@ -595,14 +777,31 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 13,
    "id": "aaea7e2f",
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
     }
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "new highest energy found:  3.1432\n",
+      "new highest energy found:  3.283599999999999\n",
+      "new highest energy found:  4.361\n",
+      "new highest energy found:  4.925600000000001\n",
+      "new highest energy found:  4.941999999999999\n",
+      "highest energy:  4.941999999999999\n",
+      "best guess mixer angles:  [0.392 0.247 0.138]\n",
+      "best guess cost angles:  [0.592 0.738 0.608]\n",
+      "CPU times: user 2min 19s, sys: 32.9 s, total: 2min 52s\n",
+      "Wall time: 43.1 s\n"
+     ]
+    }
+   ],
    "source": [
     "%%time\n",
     "qaoa_result, cost_angles, mixer_angles = solve_maxcut_instance(\n",
@@ -617,10 +816,28 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 14,
    "id": "3b86301e-7645-4553-be38-3ebf89eedd37",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Success ratio 0.4246 \n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "import matplotlib.pyplot as plt\n",
     "\n",
@@ -667,10 +884,31 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 15,
    "id": "ffce2a97-902c-44d8-8d64-b25498752907",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "G = nx.Graph()\n",
     "G.add_edges_from(max_cut_graph_edges)\n",

From 1fa4d95d92dac7b69af649228cf173bbfbb4af9a Mon Sep 17 00:00:00 2001
From: CalMacCQ <93673602+CalMacCQ@users.noreply.github.com>
Date: Tue, 24 Dec 2024 10:24:06 +0000
Subject: [PATCH 16/17] clear outputs

---
 .../pytket_qaoa_maxcut_example.ipynb          | 264 +-----------------
 1 file changed, 14 insertions(+), 250 deletions(-)

diff --git a/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb b/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb
index 7262c314..84efad7b 100644
--- a/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb
+++ b/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb
@@ -28,25 +28,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": null,
    "id": "9456fbeb",
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
     }
    },
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "<Figure size 200x200 with 1 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "import networkx as nx\n",
     "import matplotlib.pyplot as plt\n",
@@ -219,25 +208,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": null,
    "id": "688f1332",
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
     }
    },
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "import networkx as nx\n",
     "\n",
@@ -331,93 +309,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": null,
    "id": "0a9db628",
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
     }
    },
-   "outputs": [
-    {
-     "data": {
-      "text/html": [
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "<div style=\"resize: vertical; overflow: auto; height: 300px; display: block\">\n",
-       "    <iframe srcdoc=\"\n",
-       "&lt;!DOCTYPE html&gt;\n",
-       "&lt;html lang=&#34;en&#34;&gt;\n",
-       "&lt;head&gt;\n",
-       "    &lt;meta charset=&#34;UTF-8&#34;&gt;\n",
-       "    &lt;!-- Download Vue 3--&gt;\n",
-       "&lt;script type=&#34;application/javascript&#34; src=&#34;https://cdn.jsdelivr.net/npm/vue@3&#34;&gt;&lt;/script&gt;\n",
-       "&lt;!-- Download Circuit Renderer with styles --&gt;\n",
-       "&lt;script type=&#34;application/javascript&#34; src=&#34;https://unpkg.com/pytket-circuit-renderer@0.10/dist/pytket-circuit-renderer.umd.js&#34;&gt;&lt;/script&gt;\n",
-       "&lt;link rel=&#34;stylesheet&#34; href=&#34;https://unpkg.com/pytket-circuit-renderer@0.10/dist/pytket-circuit-renderer.css&#34;&gt;\n",
-       "&lt;/head&gt;\n",
-       "&lt;body&gt;\n",
-       "\n",
-       "\n",
-       "    &lt;div id=&#34;circuit-display-vue-container-35911ebf-49d7-4448-b48a-c0b4c8a3cc5a&#34; class=&#34;pytket-circuit-display-container&#34;&gt;\n",
-       "        &lt;div style=&#34;display: none&#34;&gt;\n",
-       "            &lt;div id=&#34;circuit-json-to-display&#34;&gt;{&#34;bits&#34;: [], &#34;commands&#34;: [{&#34;args&#34;: [[&#34;q&#34;, [0]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [1]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [2]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [3]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [4]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [5]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [6]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}], &#34;created_qubits&#34;: [], &#34;discarded_qubits&#34;: [], &#34;implicit_permutation&#34;: [[[&#34;q&#34;, [0]], [&#34;q&#34;, [0]]], [[&#34;q&#34;, [1]], [&#34;q&#34;, [1]]], [[&#34;q&#34;, [2]], [&#34;q&#34;, [2]]], [[&#34;q&#34;, [3]], [&#34;q&#34;, [3]]], [[&#34;q&#34;, [4]], [&#34;q&#34;, [4]]], [[&#34;q&#34;, [5]], [&#34;q&#34;, [5]]], [[&#34;q&#34;, [6]], [&#34;q&#34;, [6]]]], &#34;phase&#34;: &#34;0.0&#34;, &#34;qubits&#34;: [[&#34;q&#34;, [0]], [&#34;q&#34;, [1]], [&#34;q&#34;, [2]], [&#34;q&#34;, [3]], [&#34;q&#34;, [4]], [&#34;q&#34;, [5]], [&#34;q&#34;, [6]]]}&lt;/div&gt;\n",
-       "        &lt;/div&gt;\n",
-       "        &lt;circuit-display-container\n",
-       "                :circuit-element-str=&#34;&#39;#circuit-json-to-display&#39;&#34;\n",
-       "                :init-render-options=&#34;initRenderOptions&#34;\n",
-       "                view-format=&#34;None&#34;\n",
-       "        &gt;&lt;/circuit-display-container&gt;\n",
-       "    &lt;/div&gt;\n",
-       "    &lt;script type=&#34;application/javascript&#34;&gt;\n",
-       "      const circuitRendererUid = &#34;35911ebf-49d7-4448-b48a-c0b4c8a3cc5a&#34;;\n",
-       "      const displayOptions = JSON.parse(&#39;{&#34;zxStyle&#34;: true, &#34;condenseCBits&#34;: false}&#39;);\n",
-       "\n",
-       "      // Script to initialise the circuit renderer app\n",
-       "\n",
-       "const { createApp } = Vue;\n",
-       "const circuitDisplayContainer = window[&#34;pytket-circuit-renderer&#34;].default;\n",
-       "// Init variables to be shared between circuit display instances\n",
-       "if (typeof window.pytketCircuitDisplays === &#34;undefined&#34;) {\n",
-       "    window.pytketCircuitDisplays = {};\n",
-       "}\n",
-       "// Create the root Vue component\n",
-       "const app = createApp({\n",
-       "    delimiters: [&#39;[[#&#39;, &#39;#]]&#39;],\n",
-       "    components: { circuitDisplayContainer },\n",
-       "    data () {\n",
-       "      return {\n",
-       "        initRenderOptions: displayOptions,\n",
-       "      }\n",
-       "    }\n",
-       "})\n",
-       "app.config.unwrapInjectedRef = true;\n",
-       "app.mount(&#34;#circuit-display-vue-container-&#34;+circuitRendererUid);\n",
-       "window.pytketCircuitDisplays[circuitRendererUid] = app;\n",
-       "    &lt;/script&gt;\n",
-       "\n",
-       "\n",
-       "\n",
-       "&lt;/body&gt;\n",
-       "&lt;/html&gt;\n",
-       "\"\n",
-       "            width=\"100%\" height=\"100%\"\n",
-       "            style=\"border: none; outline: none; overflow: auto\"></iframe>\n",
-       "</div>\n",
-       "\n"
-      ],
-      "text/plain": [
-       "<IPython.core.display.HTML object>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "from pytket import Circuit\n",
     "from pytket.circuit.display import render_circuit_jupyter as draw\n",
@@ -523,89 +422,10 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": null,
    "id": "f97de321",
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/html": [
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "<div style=\"resize: vertical; overflow: auto; height: 300px; display: block\">\n",
-       "    <iframe srcdoc=\"\n",
-       "&lt;!DOCTYPE html&gt;\n",
-       "&lt;html lang=&#34;en&#34;&gt;\n",
-       "&lt;head&gt;\n",
-       "    &lt;meta charset=&#34;UTF-8&#34;&gt;\n",
-       "    &lt;!-- Download Vue 3--&gt;\n",
-       "&lt;script type=&#34;application/javascript&#34; src=&#34;https://cdn.jsdelivr.net/npm/vue@3&#34;&gt;&lt;/script&gt;\n",
-       "&lt;!-- Download Circuit Renderer with styles --&gt;\n",
-       "&lt;script type=&#34;application/javascript&#34; src=&#34;https://unpkg.com/pytket-circuit-renderer@0.10/dist/pytket-circuit-renderer.umd.js&#34;&gt;&lt;/script&gt;\n",
-       "&lt;link rel=&#34;stylesheet&#34; href=&#34;https://unpkg.com/pytket-circuit-renderer@0.10/dist/pytket-circuit-renderer.css&#34;&gt;\n",
-       "&lt;/head&gt;\n",
-       "&lt;body&gt;\n",
-       "\n",
-       "\n",
-       "    &lt;div id=&#34;circuit-display-vue-container-937d5171-df4e-4a09-b230-f802a7dc94a2&#34; class=&#34;pytket-circuit-display-container&#34;&gt;\n",
-       "        &lt;div style=&#34;display: none&#34;&gt;\n",
-       "            &lt;div id=&#34;circuit-json-to-display&#34;&gt;{&#34;bits&#34;: [[&#34;c&#34;, [0]], [&#34;c&#34;, [1]], [&#34;c&#34;, [2]]], &#34;commands&#34;: [{&#34;args&#34;: [[&#34;q&#34;, [0]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [1]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [2]]], &#34;op&#34;: {&#34;type&#34;: &#34;H&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [0]], [&#34;q&#34;, [1]]], &#34;op&#34;: {&#34;params&#34;: [&#34;-0.375&#34;], &#34;type&#34;: &#34;ZZPhase&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [1]], [&#34;q&#34;, [2]]], &#34;op&#34;: {&#34;params&#34;: [&#34;-0.375&#34;], &#34;type&#34;: &#34;ZZPhase&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [0]], [&#34;q&#34;, [1]], [&#34;q&#34;, [2]]], &#34;op&#34;: {&#34;data&#34;: &#34;&#34;, &#34;signature&#34;: [&#34;Q&#34;, &#34;Q&#34;, &#34;Q&#34;], &#34;type&#34;: &#34;Barrier&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [0]]], &#34;op&#34;: {&#34;params&#34;: [&#34;0.8&#34;], &#34;type&#34;: &#34;Rx&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [1]]], &#34;op&#34;: {&#34;params&#34;: [&#34;0.8&#34;], &#34;type&#34;: &#34;Rx&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [2]]], &#34;op&#34;: {&#34;params&#34;: [&#34;0.8&#34;], &#34;type&#34;: &#34;Rx&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [0]], [&#34;q&#34;, [1]]], &#34;op&#34;: {&#34;params&#34;: [&#34;-0.3&#34;], &#34;type&#34;: &#34;ZZPhase&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [1]], [&#34;q&#34;, [2]]], &#34;op&#34;: {&#34;params&#34;: [&#34;-0.3&#34;], &#34;type&#34;: &#34;ZZPhase&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [0]], [&#34;q&#34;, [1]], [&#34;q&#34;, [2]]], &#34;op&#34;: {&#34;data&#34;: &#34;&#34;, &#34;signature&#34;: [&#34;Q&#34;, &#34;Q&#34;, &#34;Q&#34;], &#34;type&#34;: &#34;Barrier&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [0]]], &#34;op&#34;: {&#34;params&#34;: [&#34;0.1&#34;], &#34;type&#34;: &#34;Rx&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [1]]], &#34;op&#34;: {&#34;params&#34;: [&#34;0.1&#34;], &#34;type&#34;: &#34;Rx&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [2]]], &#34;op&#34;: {&#34;params&#34;: [&#34;0.1&#34;], &#34;type&#34;: &#34;Rx&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [0]], [&#34;c&#34;, [0]]], &#34;op&#34;: {&#34;type&#34;: &#34;Measure&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [1]], [&#34;c&#34;, [1]]], &#34;op&#34;: {&#34;type&#34;: &#34;Measure&#34;}}, {&#34;args&#34;: [[&#34;q&#34;, [2]], [&#34;c&#34;, [2]]], &#34;op&#34;: {&#34;type&#34;: &#34;Measure&#34;}}], &#34;created_qubits&#34;: [], &#34;discarded_qubits&#34;: [], &#34;implicit_permutation&#34;: [[[&#34;q&#34;, [0]], [&#34;q&#34;, [0]]], [[&#34;q&#34;, [1]], [&#34;q&#34;, [1]]], [[&#34;q&#34;, [2]], [&#34;q&#34;, [2]]]], &#34;phase&#34;: &#34;0.0&#34;, &#34;qubits&#34;: [[&#34;q&#34;, [0]], [&#34;q&#34;, [1]], [&#34;q&#34;, [2]]]}&lt;/div&gt;\n",
-       "        &lt;/div&gt;\n",
-       "        &lt;circuit-display-container\n",
-       "                :circuit-element-str=&#34;&#39;#circuit-json-to-display&#39;&#34;\n",
-       "                :init-render-options=&#34;initRenderOptions&#34;\n",
-       "                view-format=&#34;None&#34;\n",
-       "        &gt;&lt;/circuit-display-container&gt;\n",
-       "    &lt;/div&gt;\n",
-       "    &lt;script type=&#34;application/javascript&#34;&gt;\n",
-       "      const circuitRendererUid = &#34;937d5171-df4e-4a09-b230-f802a7dc94a2&#34;;\n",
-       "      const displayOptions = JSON.parse(&#39;{&#34;zxStyle&#34;: true, &#34;condenseCBits&#34;: false}&#39;);\n",
-       "\n",
-       "      // Script to initialise the circuit renderer app\n",
-       "\n",
-       "const { createApp } = Vue;\n",
-       "const circuitDisplayContainer = window[&#34;pytket-circuit-renderer&#34;].default;\n",
-       "// Init variables to be shared between circuit display instances\n",
-       "if (typeof window.pytketCircuitDisplays === &#34;undefined&#34;) {\n",
-       "    window.pytketCircuitDisplays = {};\n",
-       "}\n",
-       "// Create the root Vue component\n",
-       "const app = createApp({\n",
-       "    delimiters: [&#39;[[#&#39;, &#39;#]]&#39;],\n",
-       "    components: { circuitDisplayContainer },\n",
-       "    data () {\n",
-       "      return {\n",
-       "        initRenderOptions: displayOptions,\n",
-       "      }\n",
-       "    }\n",
-       "})\n",
-       "app.config.unwrapInjectedRef = true;\n",
-       "app.mount(&#34;#circuit-display-vue-container-&#34;+circuitRendererUid);\n",
-       "window.pytketCircuitDisplays[circuitRendererUid] = app;\n",
-       "    &lt;/script&gt;\n",
-       "\n",
-       "\n",
-       "\n",
-       "&lt;/body&gt;\n",
-       "&lt;/html&gt;\n",
-       "\"\n",
-       "            width=\"100%\" height=\"100%\"\n",
-       "            style=\"border: none; outline: none; overflow: auto\"></iframe>\n",
-       "</div>\n",
-       "\n"
-      ],
-      "text/plain": [
-       "<IPython.core.display.HTML object>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "from networkx import path_graph\n",
     "\n",
@@ -777,31 +597,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": null,
    "id": "aaea7e2f",
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
     }
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "new highest energy found:  3.1432\n",
-      "new highest energy found:  3.283599999999999\n",
-      "new highest energy found:  4.361\n",
-      "new highest energy found:  4.925600000000001\n",
-      "new highest energy found:  4.941999999999999\n",
-      "highest energy:  4.941999999999999\n",
-      "best guess mixer angles:  [0.392 0.247 0.138]\n",
-      "best guess cost angles:  [0.592 0.738 0.608]\n",
-      "CPU times: user 2min 19s, sys: 32.9 s, total: 2min 52s\n",
-      "Wall time: 43.1 s\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "%%time\n",
     "qaoa_result, cost_angles, mixer_angles = solve_maxcut_instance(\n",
@@ -816,28 +619,10 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": null,
    "id": "3b86301e-7645-4553-be38-3ebf89eedd37",
    "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Success ratio 0.4246 \n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "import matplotlib.pyplot as plt\n",
     "\n",
@@ -884,31 +669,10 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": null,
    "id": "ffce2a97-902c-44d8-8d64-b25498752907",
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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W5JlnnuG9995j9+7dNGnShDvvvJNdu3YFHU3Ku9WrYfr0A5bJ/3UOcPmvvnItk+np8Nxz8UgpSflmoVRCadq0KYsWLeKvf/0rTz31FKeccgrTp08POpaUN6NH52vtyO1AHu/9jt4l/sor0Rt+JKmIWSiVcEqXLs2AAQP4+OOPqV27Nm3btiUjI4ONGzcGHU3K3fvv/3ex8oO4EqgIlCV6CvzDvOy0bx8sX17geJJUUBZKJawTTzyRGTNmMGTIEN566y3q1avHsGHD8LJgFVsffHDQO7tLA92Ap4A3gAeAj4meAl+Sl89YvDi2jJJUABZKJbSUlBR69+7NihUraNeuHaFQiDZt2vD5558HHU36rS1bDrrJmcA44CqgM9Cf6N3dKcBdB9s5PR02b44poiQVRHrQAaR4qFatGiNGjODyyy/nuuuu45RTTuHee+/ltttuo1SpUkHHUwmSnZ3Npk2b+P7773/z9UBmJqULcMw6QBfgdSAbOOBVmJEI+AAASQGwUCqptGvXjmXLlnHfffdx9913M3r0aAYPHswZZ5yR72Pt3g0LF0afcLdiRfTXpUvDCSdAkybRRykfdlj8fwYVP5mZmWzYsOEX5fDXv/7pa9OmTeT86rR2+fLlOfLII7k9LY2qBVzM/BhgH7CT6LWV+5WdDVWqFOj4khQL16FU0lqyZAnXXHMNixcv5sYbb+SBBx6gQoUKB93vyy/hmWfgxRdh27b/Pt3up+FPJBL9/3bp0nDZZXDjjdCoURH8QIqrvXv37rcQ7u9r835OIx922GEceeSRP39Vq1btF7/+369DDjkkutOFF8KbbxboCTkXA28RLZS5Xqv00UfRZ3xLUhGyUCqpZWVl8fTTT3P33Xdz+OGH89xzz9GpU6f9bpudDf/4BwwYEP3nvDyQJz09ut1NN8Hf/gY/9QYFY9euXXkuiVu3bv3N/lWqVDlgKfx1eSxTpkz+A/797/B//5frb66NQNVfvfYR0UXO2xO9UeeAypWL/i0o3ZNPkoqWhVIlwpo1a7j++uuZMmUKF198MQMHDqR69eo/v799O3TqBHPmFOz4qalw/PHRxzPXqhWn0CISibB9+/bflMEDnW7esWPHL/ZPTU3liCOOyFNJrFq1auFfb/vVV3DccbkuHdQKKEf05pxqwCfAIKAUMB+od6Ad09Ohd28YPDieiSUpTyyUKjEikQhjxozhpptuYu/evTz88MNcc8017N6dynnnRa+VjOUx4enpcNRRMH8+1KwZv9zJJhKJsGXLljxPEvfs2fOL/dPT0w94evnXrx9xxBGk5WMh8SLRqRNMmXLA32wDgZHA58A2otPK84B7id6ck6vFi+G00+KXVZLyyEKpEmfz5s3ceeedvPjii5x11llUq/YmEydWjqlM/iQ9PXo95Xvv5euBKAkvJyeHzZs356kgbtiwgX2/eppL6dKl8zRFPPLII6lcuTKpqQm84tmyZdHSl5XnZ+AcXFoa9OgBo0bF75iSlA8WSpVYs2fP5vLLR/LNN/k5RfggcDdQH1h2wK0eewxuuy3GgAHLzs5m48aNeTrVvGHDBrJ/1cjLlSuX55JYqVIlUkrScjcPPhi9ljIef/ympkLlyvDpp97hLSkwFkqVWJEI/O53OXz+OUQieZl4fQ38jugS08eSW6EsVw6++w4qHnB9l2Dsb/mbA31t2rTpN08dqlChQp5ONR955JGUL1++ZJXE/MjKgu7dYeLEAt3x/bPU1OhyA2+/DWedFb98kpRPFkqVWLNnQ8uW+dnjUqL34GYDm8itUKakwNNPQ9++sSTMm3gvf5Pbnc2HeBt7/OzbB1dcAWPGFGz/9HQoWxYmT4ZzzolvNknKJwulSqwrr4QRI/J6Kds7RO+/XQLcSF4K5e9/D0vy9PDl39q5c2eu1yAGvvyN4iMSgZdfhptvhj178nZXWFpadLu2baOLpR5zTOHnlKSDsFCqxDrxRMjbI7+zgUZAM+AFoAUHK5QQHSDt2AFlyhx4+ZsDfe3cufMXx0pNTaVq1aq5FsMiXf5G8fXNN9HV9F94Ifq879TU6N9KsrOj39PTITMzum3LltGFT7t08TGLkooNC6VKpJ07oUKFvN4T8SzwF2AV0UVcWpCXQglw8skhdu6ck+/lb379VaVKleK3/I3ib+9emDcPFi2CpUujfyNJS4subtq4MTRrFl3wVJKKGR+noBJp06a8lsn/APcA/8dvn19ycDVqnEaTJjWSc/kbxV+ZMtCqVfRLkhKIhVIlUt7n8ncDhxO9bjL/brrpFjp2LNCukiQlDAulSqTKlfOy1SqiD737B/Dt/7y+B8gE1gAViRbO/Tv8wG9JkpQ0vIZSJdYxx8DXX+e2xWzgYOsK3Uy0cP5WSgps2wblyxcknSRJicMJpUqsZs3g9ddzW6mlATB+P6/fDWwHngJOOODx69SxTEqSSgYLpUqsyy6DsWNz2+II4ML9vP6PH7/v772o1FQIhQoYTJKkBOMpb5VYWVnR097ff5/fRyq34GDLBqWnw7p1cNRRsWWUJCkRuGaJSqz0dPj73/NbJiF6beWBy2RqavTBJ5ZJSVJJ4YRSJVokAu3bw4wZeX0EY+7S0qB2bVi2DMqVi/14kiQlAieUKtFSUiAchpo1oxPL2GRRrlwO48dbJiVJJYuFUiXekUfCO+9EJ4sFfXBNWlqElJSd1Kp1JXXq7IpvQEmSijkLpUT05pzFi+GPf4z+Oq+Pzf6pgLZpk8LkyWv56qvXuPTSS8mKx/lzSZIShIVS+lHFivDPf8KcOdCuXfR0OPz2VHh6+n/fO+MMGDMGJk+Gdu1OYezYsUyePJmbbroJL0+WJJUU3pQjHcBXX8H06bBoEXz8MezcCWXKQN260LgxtGgBp5zy2/1eeukl/vjHP/LQQw9x5513FnluSZKKmoVSKgT33nsvf/3rXxkxYgS9evUKOo4kSYXKQikVgkgkwlVXXcXIkSOZOnUqrVq1CjqSJEmFxkIpFZLMzEw6duzIggULmDt3Lqfs7/y4JElJwEIpFaLt27fTvHlzNm3axPz586lZs2bQkSRJijsLpVTI1q9fT9OmTalUqRLvvvsulSpVCjqSJElx5bJBUiGrXr06U6ZMYd26dXTr1o19+/YFHUmSpLiyUEpF4OSTT+aNN97g3Xff5eqrr3aNSklSUrFQSkWkefPmDBs2jBEjRnD33XcHHUeSpLhJP/gmkuLlkksu4euvv+bPf/4ztWrVok+fPkFHkiQpZhZKqYj169ePtWvXcv3111OjRg06duwYdCRJkmLiXd5SALKzs+nRowdTp05l1qxZnHHGGUFHkiSpwCyUUkB2795N69atWbVqFfPnz+eEE04IOpIkSQVioZQCtGnTJs466ywikQjvvfceRxxxRNCRJEnKN+/ylgJ0xBFHMGXKFLZu3UqnTp3YtWtX0JEkSco3C6UUsOOPP5633nqLpUuX0qtXL7Kzs4OOJElSvlgopWKgSZMmjBkzhokTJ3LLLbe48LkkKaFYKKVi4oILLuD555/nmWee4fHHHw86jiRJeeY6lFIxcu2117J27Vpuv/12atasyaWXXhp0JEmSDsq7vKViJhKJ0Lt3b1555RWmTZtGixYtgo4kSVKuLJRSMbRv3z4uuOACPvjgA+bNm0f9+vWDjiRJ0gFZKKViatu2bZxzzjn88MMPLFiwgKOPPjroSJIk7Zc35UjFVMWKFZk8eTKRSIQOHTqwbdu2oCNJkrRfFkqpGKtRowZTpkxhzZo1XHzxxWRmZgYdSZKk37BQSsVcgwYNmDBhAnPmzOGaa65xjUpJUrFjoZQSQIsWLRg6dCjhcJh777036DiSJP2C61BKCaJnz56sW7eOO++8k2OOOYZrrrkm6EiSJAEWSimh3H777axdu5brrruOGjVq0KFDh6AjSZLkskFSosnOzqZbt25Mnz6dOXPm0KRJk6AjSZJKOAullIB27drFeeedxxdffMH8+fM5/vjjg44kSSrBLJRSgtq4cSNnnnkmqampvPfee1SpUiXoSJKkEsq7vKUEVbVqVaZOncoPP/xA586d2b17d9CRJEkllIVSSmAnnHACkyZNYsmSJVx++eVkZ2cHHUmSVAJZKKUEd8YZZ/DKK68wYcIE+vXr58LnkqQiZ6GUkkDnzp159tlnGThwIE8++WTQcSRJJYzrUEpJ4k9/+hNfffUVt912GzVr1qRHjx5BR5IklRDe5S0lkZycHDIyMhg7dizTp0+nefPmQUeSJJUAFkopyezbt4/27duzePFi3nvvPerVqxd0JElSkrNQSklo69atnHPOOWzbto358+dTvXr1oCNJkpKYN+VISahSpUpMnjyZrKwsLrjgArZv3x50JElSErNQSkmqZs2aTJkyhdWrV9O9e3cyMzODjiRJSlIWSimJnXLKKYwfP56ZM2fSp08f16iUJBUKC6WU5Fq1asXLL7/MkCFD+Otf/xp0HElSEnIdSqkEuPzyy1m3bh0DBgzgmGOO4aqrrgo6kiQpiVgopRKif//+rF27lmuvvZajjz6adu3aBR1JkpQkXDZIKkGysrK46KKLmDVrFnPmzKFRo0ZBR5IkJQELpVTC7Ny5k5YtW7Ju3Trmz5/PscceG3QkSVKCs1BKJdCGDRto1qwZpUuXZt68eRx++OFBR5IkJTDv8pZKoGrVqjF16lQ2btxIly5d2LNnT9CRJEkJzEIplVAnnngikyZN4sMPPyQjI4OcnJygI0mSEpSFUirBmjZtyujRoxk3bhy333570HEkSQnKQimVcBdeeCFPP/00TzzxBE899VTQcSRJCch1KCXRt29fvvrqK2699VZq1qxJt27dgo4kSUog3uUtCYCcnBx69erF+PHjmTFjBmeddVbQkSRJCcJCKelne/fu5fzzz+fjjz9m3rx51K1bN+hIkqQEYKGU9Atbtmzh7LPPZufOncyfP5+jjjoq6EiSpGLOm3Ik/cJhhx3G5MmT2bdvHx07dmTHjh1BR5IkFXMWSkm/UatWLd566y0+++wzevToQVZWVtCRJEnFmIVS0n41bNiQ1157jenTp3Pdddfh1TGSpAOxUEo6oDZt2vDiiy/y4osv8uCDDwYdR5KKj5wcWL8e1qyB776DEv6XbtehlJSrUCjEunXr+L//+z9q1qxJ7969g44kScH49lt48UX4179gyRLYteu/71WoAI0aQYcOcOWVULVqcDkD4F3ekg4qEonQp08fhgwZwltvvUXbtm2DjiRJRef77+HWW+HVVyElBbKzD7xtamr0q3dveOQRqFy5yGIGyUIpKU+ysrLo0qUL77zzDu+++y4NGzYMOpIkFb5x4+CPf4QdO3Ivkr+WlgZVqsCwYXD++YWXr5iwUErKsx07dtCiRQu+/fZbFixYQK1atYKOJEmFZ+BAuPnm6FSyIHUpNTW6XzgMV1wR/3zFiIVSUr58//33NGvWjHLlyjF37lwql5DTOZJKmJEj4fLL43OslBSYNCl6fWWSslBKyrdPP/2UM888k1NOOYVp06ZRpkyZoCNJUvysWwf16sHOnfE5XkoKHH44fPpp9DR4EnLZIEn59rvf/Y6JEyeyYMECevfuTU5OTtCRJCl++vSBvXv3+9YHwA1AfeBQoBbQA/gst+NFIrBlC/TrF9+cxYgTSkkF9tprr9G9e3f+/Oc/88gjjwQdR5Ji98knUL/+Ad++GJgHdAdOBb4DngF2AAuABrkdOzU1Ov08+ui4xS0unFBKKrBu3brxj3/8g0cffZSnn3466DiSFLvnn4f0Ay/T3Q/4ChgI/BG4G3gXyAIeOtixU1Jg8OD45CxmnFBKitltt93Gk08+yWuvvUbXrl2DjiNJBVe7Nqxdm+/dGv/4fdFBN2wMH36Y7+MXdxZKSTHLycmhZ8+eTJw4kZkzZ9KsWbOgI0lS/m3ZUqCFyCPAMUSvq5x2sI1Ll47e7JPLFDQRecpbUsxSU1MJh8OcfvrpdOrUic8+y/XydEkqnlauLNBuI4FvgEvysvG+fdHnfycZC6WkuChbtiwTJkygWrVqtG/fng0bNgQdSZLyZ/fufO+yEugLNANCed3pf58BniQslJLi5vDDD2fKlCns2rWLjh07sjNea7hJUlEoXTpfm38HXABUAsYBaYX0OYnAQikprmrXrs3kyZNZsWIFl156KVlZWUFHkqS8Of74PG+6FWgPbAGmAnleCCg1NXrjT5KxUEqKu9NOO41x48YxZcoU+vbti/f+SUoI1atD1aoH3WwP0InoYuaTgJPz8xm/+x2UK1egeMWZhVJSoTj//PMZPHgwgwYN4u9//3vQcSQpb1q3zvUO7GyiN9/MB8YSvXYyz9LToW3bmOIVV8l1z7qkYuXKK69k7dq1/OUvf+GYY47hiiuuCDqSJOXuuutg9OgDvn0bMJHohHIzMOJX71+e27GzsuDaa2NNWCy5DqWkQhWJRPjjH//IsGHDmDJlCq1btw46kiQdWCQCDRvC8uWQnf2bt1sAc3Lb/UBvpKdD8+YwY0bMEYsjC6WkQpeZmUnnzp2ZN28ec+fO5dRTTw06kiQd2KJFcMYZkJMTv2OWKQPLlkGdOvE7ZjHiNZSSCl2pUqUYM2YMderUoUOHDqxbty7oSJJ0YI0bk3P33fE95uOPJ22ZBAulpCJSoUIF3nrrLdLT02nfvj1btmwJOpIk7VdmZia9Pv2Ul8jlFHZ+3HEHXH99PI5UbFkoJRWZ6tWrM2XKFL799lu6du3K3r17g44kSb+wb98+evbsybjXXuOwMWNIuftuSEmBtDwvWx6Vnh79euwxeOih6DGSmNdQSipy7777Lm3atKFbt24MHz6c1FT/bispeHv37qV79+5MnTqVcePG0blz5+gbCxdCKBR91nd6evRu7QP56f1GjSAchgYNiiZ8wPxTXFKRO+eccxg+fDijRo3iL3/5S9BxJIndu3dz4YUX8q9//Ys33njjv2USojfoLF8O06dDx45QocL+D1KpElx8Mbz7Lnz4YYkpk+CEUlKAnnzySfr168ezzz7L9Ul+fZGk4mvXrl106dKFefPmMXHixIMvbxaJwBdfwKpVsHcvlC0LdetCrVpJf2r7QCyUkgJ1yy238PTTTzN+/PhfTgQkqQjs2LGDTp068cEHHzBp0iRatGgRdKSEZKGUFKjs7GwuueQSJk+ezKxZs/jDH/4QdCRJJcS2bdvo0KEDS5cuZfLkyZx99tlBR0pYFkpJgdu9ezdt2rTh008/Zf78+dRJ4rXaJBUPW7ZsoV27dqxcuZKpU6fStGnToCMlNAulpGLhP//5D2eddRZZWVnMnz+fqlWrBh1JUpLavHkzbdu25YsvvmD69Ok0btw46EgJz7u8JRULVapUYcqUKezYsYOOHTuya9euoCNJSkIbN26kVatWfPXVV8yaNcsyGScWSknFxnHHHcekSZNYvnw5PXv2JDs7O+hIkpLId999R8uWLVm/fj2zZs3i97//fdCRkoaFUlKx0qRJE8aMGcNbb73FjTfeiFflSIqHb7/9lhYtWrB582bmzJlDgxK0RmRRsFBKKnY6dOjACy+8wPPPP88jjzwSdBxJCW7dunWce+657Ny5kzlz5lC3bt2gIyWd9KADSNL+/PGPf2Tt2rX079+fY445hssuuyzoSJIS0Jo1a2jVqhU5OTm88847HHfccUFHSkre5S2p2IpEIlx55ZWMGjWKadOm0bJly6AjSUogq1evpmXLlpQqVYpZs2ZRq1atoCMlLQulpGItMzOTCy64gPfff5+5c+dyyimnBB1JUgL49NNPadWqFeXLl2fmzJnUqFEj6EhJzUIpqdjbtm0bzZs35z//+Q/z58+nZs2av9wgEoF//xsWLIDFi+H776OvHXYYnHYanH46NGsG6V7lI5UEn3zyCa1ataJKlSq8/fbbVK9ePehISc9CKSkhfPvttzRt2pTKlSvzzjvvUKlSJdi3D4YMgYED4ZNPICUF0tIgKyu6U1patFjm5ED16tC3L1x/PVSuHOwPI6nQLF26lNatW3PUUUfx9ttvU61ataAjlQgWSkkJY/ny5Zx99tk0btyYKQ8+SKkrr4SVK6Nv5uWPstRUqFIFXn4ZOnYs3LCSitzixYtp06YNtWvXZvr06VSpUiXoSCWGhVJSQpkzZw7h885jcE4OqamppOR38fPU1OjE8o474KGHolNNSQlv4cKFnH/++Zx44olMmzaNyp6JKFJeUCQpoZy7di3nZmcTgfyXSYiWSYBHHoHsbHjssbjmk1T03nvvPdq1a0eDBg2YMmVK9JIYFSknlJISx7Jl0ZtsfrpGMh7GjIHu3eN3PElF6p133qFDhw40btyYSZMmUaFChaAjlUg+KUdSYsjKgssvP+Dby4HuwPHAIcARQHPgzdyOmZICffrAhg1xDCqpqMyYMYN27drxhz/8gcmTJ1smA2ShlJQYXn0VPvrogNPJr4DtQAh4Cvi/H1/vDAw60DEjEdi2zdPeUgKaNm0aHTt2pHnz5kyaNIlDDz006Eglmqe8JSWGpk3hgw/+ew1kHmQDjYE9wMrcNqxUCdavh3LlYssoqUhMmjSJbt260bZtW8aOHUvZsmWDjlTiOaGUVPx98QW8/36+yiRAGnAMsOVgG27dClOnFiybpCI1fvx4LrroIi644AJee+01y2QxYaGUVPwtXJjnTXcCm4DVwJPAFOC8g+1UqlS+PkNSMMaMGUP37t3p2rUrr776KqVLlw46kn7kskGSir8lS6KlLzPzoJveBvzzx39OBS4CnjnYTllZ8OGHMUWUVLhGjBhBKBSiZ8+eDB06lHQfpVqs+F9DUvG3aVPenoQD3AJcDHwLjCF6HeW+g+0UiXint1SMDRkyhKuvvppQKMSLL75IWlpa0JH0K57yllT85ePewbpAayADmATsADoBBz2C9ydKxdKgQYO46qqruOaaa3jppZcsk8WUhVJS8XfEEQV+ROLFwAfAZwfbsFq1Ah1fUuF55pln6NOnDzfccAMvvPACqanWluLK/zKSir/TTsvT9ZP7s/vH71tz26hUKWjSpEDHl1Q4nnjiCW688Ub69evHwIEDSSngXypVNCyUkoq/M8446Cb7uwIyExgGlANOzm3nzEw21K5doGiS4u+hhx7itttuo3///jz22GOWyQTgwuaSEsMZZ8CiRQdci7IrsI3o4xZrAN8BI4kuaP440C+XQ28DjgT+cO65hEIhLr74Yh/hJgXkr3/9K/feey/33HMP9913n2UyQTihlJQYbrwx14XNLyH6B9rzwHXAE0BN4A1yL5OkpVHuxhsZNGwY6enpXH311Rx11FFkZGQwY8YMcvK5mLqkgolEItx9993ce++9PPDAA/y///f/LJMJxAmlpMSQmQmNGsGKFZCdHZ9jpqRAxYqwciUcdRQAa9euZcSIEQwdOpRVq1ZxzDHHcMUVVxAKhTjppJPi87mSfiESiXDnnXfy6KOP8sgjj3D77bcHHUn5ZKGUlDg++ggaN45foQQYNQp69vzNy5FIhAULFhAOh3nllVfYunUrzZo1IxQKcckll3DYYYfFL4NUgkUiEW699Vaeeuop/vGPf3DzzTcHHUkFYKGUlFhefhmuvjo+x7rpJvjHPw66JNGePXuYOHEi4XCYqVOnUqpUKbp06UIoFKJt27Y+sUMqoJycHG644Qaef/55nnvuOa677rqgI6mALJSSEs9LL8E110Bqav6nlSkp0UXMb70VHnsseox8WL9+PSNHjiQcDrNs2TKOOuooevXqRSgU4pRTTslfFqkEy8nJ4dprr+Xll19m8ODBXB2vvygqEBZKSYlp4UK44gpYtSr667z8UZaWBpUqweDBcNFFMX18JBJhyZIlhMNhRo0axaZNm2jUqBGhUIjLLruMI444IqbjS8ksOzubq666ihEjRjBkyBAyMjKCjqQYWSglJa69e6PlcODAaLFMSYmWxqys6Ps/PaItOxuqVoXrr4/eLV6lSlxj7Nu3j8mTJxMOh5k0aRIAF1xwAb1796ZDhw6ULl06rp8nJbKsrCyuuOIKxo4dy/Dhw+m5n2uYlXgslJISXyQCH3wA778fXavyu++iSwxVqQING0afgtO8efSJOIVs06ZNjB49mnA4zKJFi6hSpQqXXXYZoVCIRo0auQyKSrR9+/Zx2WWX8cYbb/DKK6/QrVu3oCMpTiyUklRIli1bRjgcZsSIEXz33XfUr1+f3r1706tXL6pXrx50PKlI7d27lx49ejBlyhTGjRtH586dg46kOLJQSlIhy8rKYvr06YTDYSZMmEBmZibnn38+oVCILl26ULZs2aAjSoVqz549XHTRRcycOZPXX3+dDh06BB1JcWahlKQitGXLFsaMGcPQoUOZP38+lSpV4pJLLqF37940bdrUU+JKOrt27aJLly7MmzePN954gzZt2gQdSYXAQilJAfnss88YNmwYw4YNY926dZx44omEQiGuuOIKatWqFXQ8KWY7duygU6dOfPDBB0yaNIkWLVoEHUmFxEIpSQHLyclh9uzZDB06lNdee43du3fTsmVLQqEQ3bp149BDDw06opRv27Zto0OHDixdupTJkydz9tlnBx1JhchCKUnFyPbt23nttdcIh8PMnj2b8uXLc/HFFxMKhWjevDmp+VyIXQrCli1baNeuHStXrmTq1Kk0bdo06EgqZBZKSSqm1qxZ8/Mp8dWrV3PsscdyxRVXkJGRQZ06dYKOJ+3X5s2badu2LV988QX/+te/aNKkSdCRVAQslJJUzEUiEebNm0c4HGbMmDFs27aNs88+m1AoRPfu3alUqVLQESUANm7cSJs2bfjmm2+YPn06DRs2DDqSioiFUpISyO7du5kwYQLhcJjp06dTunRpunbtSigUonXr1qT99HQgqYh9//33nHfeeWzcuJEZM2bQoEGDoCOpCFkoJSlBffPNN4wYMYJwOMyKFSs4+uijueKKKwiFQtSrVy/oeCpBvv32W8477zy2bt3KzJkzqVu3btCRVMQslJKU4CKRCB9++CHhcJhRo0bxww8/cPrppxMKhbj00kupEudnl0v/a926dbRq1Yo9e/Ywc+ZMTjzxxKAjKQAWSklKInv37mXSpEmEw2EmT55MamoqnTp1onfv3rRr145SRfA8c5Uca9asoVWrVuTk5DBr1iyOO+64oCMpIBZKSUpSGzZsYNSoUYTDYf79739TtWpVevXqRSgU8mYJxWz16tW0atWK9PR0Zs6cSe3atYOOpABZKCWpBPjoo48Ih8OMHDmSDRs2cOqppxIKhejVqxdHHnlk0PGUYD799FNatWpF+fLlmTlzJjVq1Ag6kgJmoZSkEiQzM5Np06YRDoeZOHEi2dnZtG/fnlAoRKdOnShTpkzQEVXMffLJJ5x33nkcfvjhvP3221SvXj3oSCoGLJSSVEJt3ryZV155hXA4zMKFC6lcuTKXXnopvXv35vTTTyclJSXoiCpmli5dSuvWrTnqqKN4++23qVatWtCRVExYKCVJrFixgmHDhjF8+HC++eYb6tatSygU4vLLL6dmzZpBx1MxsHjxYtq0aUPt2rWZPn26qwfoFyyUkqSfZWdnM3PmTIYOHcr48ePZs2cPrVu3JhQK0bVrVw455JCgIyoAH3zwAW3btuXEE09k2rRpVK5cOehIKmYslJKk/dq2bRtjx44lHA7z7rvvUqFCBXr06EEoFOLss8/2lHgJ8d5779G+fXvq16/PlClTfNSn9stCKUk6qNWrVzN8+HDC4TBr1qzh+OOPJyMjg4yMDNceTGLvvPMOF1xwAY0aNWLSpElUqFAh6EgqpiyUkqQ8y8nJ4d133yUcDjN27Fh27NjBueeeSygU4uKLL7ZwJJEZM2bQuXNnmjZtysSJEzn00EODjqRizEIpSSqQnTt3Mn78eIYOHcrMmTMpV64cF110EaFQiJYtW5KWlhZ0RBXQtGnTuPDCC2nevDkTJkygXLlyQUdSMWehlCTFbN26dT+fEv/ss8+oWbMmGRkZhEIhTjrppKDjKR8mTZpEt27daNOmDePGjaNs2bJBR1ICsFBKkuImEonw/vvvEw6HeeWVV9iyZQtNmzYlFApxySWXeHdwMTd+/HguueQSOnbsyCuvvELp0qWDjqQEYaGUJBWKPXv2MHHiRMLhMNOmTSM9PZ0uXboQCoVo27Yt6enpQUfU/xgzZgyXXXYZF110ESNHjqRUqVJBR1ICsVBKkgrdd999x8iRIxk6dCjLli3jqKOOolevXoRCIU455ZSg45V4I0eOJCMjg549ezJ06FDLvvLNQilJKjKRSIQlS5YQDocZNWoUmzZt4rTTTiMUCnHZZZdRtWrVoCOWOEOHDuWqq64iFArx4osvejOVCsRCKUkKxL59+5gyZQrhcJhJkyYRiUS44IILCIVCXHDBBV6/VwQGDRpEnz59uPbaa3n++edJTU0NOpISlIVSkhS4TZs2MXr0aMLhMIsWLaJKlSr07NmT3r1706hRI5/KUwieffZZbrjhBm644QYGDhzov2PFxEIpSSpWli9fTjgcZsSIEaxfv5769esTCoW4/PLLqV69etDxksKTTz5Jv379uPXWW3n88cctk4qZhVKSVCxlZWXx9ttvM3ToUCZMmEBmZiZt27YlFArRpUsXF9suoIcffpj+/fvTv39//va3v1kmFRcWSklSsbdlyxbGjBlDOBzmvffeo1KlSlxyySWEQiGaNWtmKcqj+++/n3vuuYd77rmH++67z39vihsLpSQpoaxatYphw4YxbNgw1q5dy4knnkhGRgYZGRnUqlUr6HjFUiQS4Z577uGBBx7ggQce4C9/+UvQkZRkLJSSpISUk5PD7NmzCYfDjBs3jt27d9OyZUtCoRAXXXQR5cuXDzpisRCJRLjzzjt59NFHeeSRR7j99tuDjqQkZKGUJCW8HTt28NprrzF06FBmz57NoYceysUXX0zv3r1p3rx5iV0OJxKJcOutt/LUU0/xj3/8g5tvvjnoSEpSFkpJUlJZs2YNw4cPJxwOs3r1amrXrv3zKfE6deoEHa/I5OTkcMMNN/D888/z3HPPcd111wUdSUnMQilJSkqRSIT33nuPoUOHMmbMGLZt28ZZZ51FKBSiR48eVKpUKeiIhSYnJ4c+ffrw0ksvMXjwYK6++uqgIynJWSglSUlv9+7dTJgwgXA4zPTp0yldujRdu3YlFArRunXrpHrcYHZ2NldddRUjRoxgyJAhZGRkBB1JJYCFUpJUonz77beMGDGCcDjMJ598wtFHH83ll19OKBTi5JNPDjpeTLKyssjIyGDMmDEMHz6cnj17Bh1JJYSFUpJUIkUiET788EPC4TCjR49m8+bNNGnShN69e3PppZdSpUqVoCPmS2ZmJj179uSNN95g9OjRXHzxxUFHUglioZQklXh79+7lrbfeIhwOM3nyZFJSUujUqROhUIj27dtTqlSpQs+wbh3MnAmLFsHKlbB7N5QtC3XrQuPG0KoVHGiZzb1793LJJZcwefJkxo4dS5cuXQo9r/S/LJSSJP2PDRs2MGrUKMLhMP/+97+pWrUql112Gb1796Zhw4Zx/7w5c+Cxx+CttyASgVKlIDPzv+//9OuUFGjfHv78Z2jZ8r/v79mzh27dujFjxgxef/11OnToEPeM0sFYKCVJOoClS5cSDocZOXIk33//PaeeeiqhUIhevXpx5JFHxnTsrVuhXz94+WVIT4esrIPv89N2vXvDk09C6dK7uPDCC5k7dy5vvPEGbdq0iSmTVFAWSkmSDiIrK4tp06YxdOhQJk6cSHZ2Nu3atSMUCtGpUyfKli2br+N9+WV0yvj115Cdnf88aWlQvXoONWpcwbJlbzBp0iRatGiR/wNJcWKhlCQpHzZv3syrr75KOBzm/fffp3Llylx66aWEQiHOOOMMUlJSct3/66/hD3+ADRvyNpU8sCxSUjYyduzXdOt2eiwHkmJmoZQkqYBWrlxJOBxm+PDhfPPNN9StW5eMjAyuuOIKatas+Zvtc3LgnHNg4cJYy2RUWlqE009PYe7c6NRSCoqFUpKkGGVnZzNz5kzC4TCvv/46e/bsoXXr1oRCIbp27cohhxwCwMCBkPvjtHcAjwLvAwuBH4AhQO9cP/+JJ+DWW+Pwg0gFZKGUJCmOtm3bxrhx4xg6dCjvvvsuFSpUoHv37lx66ZV0734WW7fmdkp8DXAcUAs4HphNXgpl+fLw3Xdw6KFx+RGkfLNQSpJUSL744guGDRvGsGHD+PLL5sDQg+yxl+hU8ijgQ+B08lIoAV58EXxkt4JioZQkqZDl5OTQpMlWliypBKTmca+8F8qUlOi1mXPmxBRTKrC8/q6WJEkFlJKSyqpVlSms/+1GIvDhh9GbfqQgWCglSSpkX34JO3YU7mfs2gVffFG4nyEdiIVSkqRCtnlz0XzOpk1F8znSr1koJUkqZAdZ6zxuUv2/ugLibz1JkgrZEUcUzedUrVo0nyP9moVSkqRCVqsWVKxYuJ9RoQIce2zhfoZ0IBZKSZIKWUoKNGtWeKekU1OjzwcvqlPr0q+lBx1AkqSSoHdvmDYtL1s+A2wBvv3x128CX//4zzcClX6zR05O9PhSUFzYXJKkIrBvH1Svnpc7vo8FvjrAe1/++P4vVa4M69dDmTKxJJQKzlPekiQVgdKl4dFH87LlGiBygK9j97vHQw9ZJhUsJ5SSJBWRSATatYMZMyA7O/bjpafDuefC9OleP6lgWSglSSpCGzdGb9D56ivIyir4cdLT4ZhjYP58OPLI+OWTCsJT3pIkFaGqVeHdd+Gkkwp+13dqKtSpA3PnWiZVPFgoJUkqYtWrw4cfwm23RU9Vp+d5zZVMIMKtt8LixXD00YUYUsoHT3lLkhSgf/8bnnoKRo2K3gmenh5dBignJzqJTE2NnhovVSpCxYpvUbv2GyxaNDjo2NIvWCglSSoGfvgB5s2LTi4//RT27o3euX3SSdCkCZx1FsyZM56LLrqIefPmceaZZwYdWfqZhVKSpASRk5NDgwYNOOGEE3jzzTeDjiP9zGsoJUlKEKmpqdx1111MmjSJpUuXBh1H+pkTSkmSEkhmZiYnnngiZ555JqNGjQo6jgQ4oZQkKaGUKlWKO+64g1dffZXPP/886DgS4IRSkqSEs3v3bo499lguvPBC/vnPfwYdR3JCKUlSoilXrhz9+vVj6NChfPvtt0HHkSyUkiQlouuuu45y5crxxBNPBB1FslBKkpSIKlasyA033MALL7zAf/7zn6DjqISzUEqSlKBuvvlmcnJyePrpp4OOohLOQilJUoKqWrUq11xzDQMHDmT79u1Bx1EJZqGUJCmB3XbbbWzfvp1BgwYFHUUlmMsGSZKU4K666iqmTp3Kl19+SZkyZYKOoxLICaUkSQnuzjvv5LvvviMcDgcdRSWUE0pJkpJA9+7dWbJkCStXriQ9PT3oOCphnFBKkpQE7rrrLlavXs3YsWODjqISyAmlJElJol27dnz77bd89NFHpKSkBB1HJYgTSkmSksSAAQP4+OOPeeutt4KOohLGCaUkSUkiEolw9tlnE4lEmDdvnlNKFRknlJIkJYmUlBQGDBjA/Pnzeeedd4KOoxLECaUkSUkkEonQsGFDjjrqKKZNmxZ0HJUQTiglSUoiKSkp3HXXXfzrX/9i0aJFQcdRCeGEUpKkJJOdnU3dunX5/e9/z7hx44KOoxLACaUkSUkmLS2NO+64g9dff52VK1cGHUclgBNKSZKS0N69ezn++ONp27YtQ4YMCTqOkpwTSkmSklCZMmW47bbbGDFiBGvXrg06jpKchVKSpCR17bXXUrFiRR577LGgoyjJWSglSUpS5cuX56abbmLw4MFs2LAh6DhKYhZKSZKS2I033khaWhpPPfVU0FGUxCyUkiQlscMPP5w//elPPPPMM2zdujXoOEpSFkpJkpJcv3792LNnD88//3zQUZSkXDZIkqQS4E9/+hPjx49nzZo1lCtXLug4SjJOKCVJKgFuv/12Nm3axMsvvxx0FCUhJ5SSJJUQvXr1Yu7cuXz++eeUKlUq6DhKIk4oJUkqIfr378/atWsZNWpU0FGUZJxQSpJUgnTu3JlVq1axfPlyUlOdKyk+/J0kSVIJctddd7Fy5UomTJgQdBQlESeUkiSVMC1btmTHjh0sXLiQlJSUoOMoCTihlCSphLnrrrv48MMPefvtt4OOoiThhFKSpBImEolw+umnU7FiRWbOnBl0HCUBJ5SSJJUwKSkpDBgwgFmzZrFgwYKg4ygJOKGUJKkEysnJoX79+px00km88cYbQcdRgnNCKUlSCZSamkr//v2ZOHEiH3/8cdBxlOCcUEqSVEJlZmZSp04dzj77bEaOHBl0HCUwJ5SSJJVQpUqV4vbbb+eVV17hiy++CDqOEpgTSkmSSrBdu3Zx7LHHctFFF/HCCy8EHUcJygmlJEkl2CGHHMKtt97KkCFDWL9+fdBxlKAslJIklXDXX389ZcuW5Yknngg6ihKUhVKSpBKuUqVK9O3blxdeeIHNmzcHHUcJyEIpSZK45ZZbyMrK4plnngk6ihKQN+VIkiQAbrzxRkaNGsVXX31F+fLlg46jBOKEUpIkAfDnP/+Zbdu2MXjw4KCjKME4oZQkST/r3bs306dP54svvqBMmTJBx1GCcEIpSZJ+duedd7J+/XqGDx8edBQlECeUkiTpF7p168bSpUtZuXIlaWlpQcdRAnBCKUmSfuGuu+7i888/Z9y4cUFHUYJwQilJkn6jbdu2bNiwgSVLlpCSkhJ0HBVzTiglSdJvDBgwgI8++ogpU6YEHUUJwAmlJEn6jUgkwplnnklaWhpz584NOo6KOSeUkiTpN1JSUhgwYADz5s3j3XffDTqOijknlJIkab9ycnJo2LAhNWrU8NS3cuWEUpIk7Vdqair9+/dn6tSpLF68OOg4KsacUEqSpAPKysrid7/7HY0bN2bMmDFBx1Ex5YRSkiQdUHp6OnfccQfjxo3j008/DTqOiiknlJIkKVd79uzh+OOPp3379rz00ktBx1Ex5IRSkiTlqmzZsvTr149hw4axbt26oOOoGLJQSpKkg+rTpw8VKlTg8ccfDzqKiiELpSRJOqgKFSpw4403MmjQIDZu3Bh0HBUzFkpJkpQnN910E6mpqQwcODDoKCpmLJSSJClPqlSpQp8+fXj66afZtm1b0HFUjFgoJUlSnvXr149du3bx/PPPBx1FxYjLBkmSpHy59tprmThxIl9++SXlypULOo6KASeUkiQpX+644w42btzIkCFDgo6iYsIJpSRJyreePXuyYMECPvvsM0qVKhV0HAXMCaUkScq3/v37s2bNGl555ZWgo6gYcEIpSZIKpGPHjnz55Zd8/PHHpKY6oyrJ/K8vSZIK5K677uKTTz5h4sSJQUdRwJxQSpKkAjv33HPZs2cPCxYsICUlJeg4CogTSkmSVGADBgxg4cKFzJw5M+goCpATSkmSVGCRSITGjRtTuXJlZsyYEXQcBcQJpSRJKrCUlBQGDBjAzJkzef/994OOo4A4oZQkSTHJzs7m5JNPpl69ekyYMCHoOAqAE0pJkhSTtLQ0+vfvzxtvvMHy5cuDjqMAOKGUJEkx27dvHyeccAItWrRg+PDhQcdREXNCKUmSYla6dGluv/12Ro8ezZdffhl0HBUxJ5SSJCkudu3aRe3atenevTvPPfdc0HFUhJxQSpKkuDjkkEO45ZZbePnll/nuu++CjqMiZKGUJElx07dvX0qXLs2TTz4ZdBQVIQulJEmKm8MOO4zrr7+e5557jh9++CHoOCoiFkpJkhRXt956K1lZWTz77LNBR1ER8aYcSZIUd3379uXVV1/lq6++4tBDDw06jgqZE0pJkhR3t99+O1u2bOHFF18MOoqKgBNKSZJUKDIyMpg1axarV6+mdOnSQcdRIXJCKUmSCkX//v35+uuvGTFiRNBRVMicUEqSpELTtWtXli9fzooVK0hLSws6jgqJE0pJklRo7rrrLlatWsVrr70WdBQVIieUkiSpULVp04ZNmzaxePFiUlJS4IcfYPFi+O47yMmBSpXg97+HWrUgJSXouCoAC6UkSSpUM2fOpMd55zH3yiup+847sHr1/jesXBkuuwyuuw7q1y/akIqJhVKSJBWerCwijzxC1t13kxaJHPxau/R0yMqCHj3gmWegatWiSKkYWSglSVLhWLcOLrwQliyB/NaNtDSoWBFefRXatCmUeIofC6UkSYq/tWvhzDPh+++jE8eCSEmJFsvx46Fjx/jmU1xZKCVJUnzt3g0NG8IXXxS8TP4kJSV6GvzDD+HUU+MST/HnskGSJCm+7rkHPv/8gGVyL3AncDRQDvgDMP1Ax4pEoneCX345ZGYWRlrFgYVSkiTFzyefwOOPR0vgAfQGngB6AU8BaUAHYO6BdsjOhmXL4Lnn4ptVceMpb0mSFD99+8KgQQecTi4kOpF8FPjzj6/tARoA1YD3cjv2scdGlxxKdR5W3PhfRJIkxcfu3TBkSK7XTY4jOpG89n9eKwtcDcwH1uV2/DVrYNas2HMq7iyUkiQpPpYsiZbK3DYBTgIq/ur1M378/u/cdk5Ph3feKWg6FSILpSRJio9Fiw766MT1QPX9vP7Ta9/mtnN2NnzwQcGyqVBZKCVJUnx88UV0ipiL3UCZ/bxe9n/eP6BIBD77rGDZVKgslJIkKT7ysKxPOaLLBv3anv95P9bPUNGzUEqSpPg49NCDblKd6GnvX/vptaMPdoDy5fOXSUXCQilJkuKjfv2DThAbAp8B2371+vv/8/4BpaVFn8CjYsdCKUmS4qNx44NucjGQDQz6n9f2AkOIrk95TG47RyJ5+gwVPRc2lyRJ8ZGTA8cdB2vX5rpZD2A8cCtQBwgTXfB8BtD8YJ+xciX87nexZ1VcOaGUJEnxkZoKN9xw0CfZDANuAYYDNwGZwCQOUibT0qBFC8tkMeWEUpIkxc/mzXDCCbB1a/QUdTz961/Qpk18j6m4cEIpSZLi5/DD4YUX4lsm09Kgd2/LZDHmhFKSJMVXJBItgMOHx14s09Ohdm348EM47LB4pFMhcEIpSZLiKyUFXnwRunY96KMYc5WWBsccA7NmWSaLOQulJEmKv1KlYMwYuOeeaDFMS8v7vj+V0A4dYMGCaKlUsWahlCRJhSMtDe67L3q6+uyzo6/l9qzvn9479lgYORLeeAOqVSvslIoDr6GUJElFY8UKGDoU5s2DxYth9+7o62lpULcuNG0Kl1wC55130KWHVLxYKCVJUtHLyYFduyA7Gw45JHqKXAnLQilJkqSYOE+WJElSTCyUkiRJiomFUpIkSTGxUEqSJCkmFkpJkiTFxEIpSZKkmFgoJUmSFBMLpSRJkmJioZQkSVJMLJSSJEmKiYVSkiRJMbFQSpIkKSYWSkmSJMXEQilJkqSYWCglSZIUEwulJEmSYmKhlCRJUkwslJIkSYqJhVKSJEkxsVBKkiQpJhZKSZIkxcRCKUmSpJhYKCVJkhQTC6UkSZJiYqGUJElSTCyUkiRJiomFUpIkSTGxUEqSJCkmFkpJkiTFxEIpSZKkmFgoJUmSFBMLpSRJkmJioZQkSVJMLJSSJEmKiYVSkiRJMbFQSpIkKSYWSkmSJMXk/wOilQlvQZhVjgAAAABJRU5ErkJggg==",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "G = nx.Graph()\n",
     "G.add_edges_from(max_cut_graph_edges)\n",

From 89fc450f1a2ad9fc68b8e860e83be6dc58d77df2 Mon Sep 17 00:00:00 2001
From: CalMacCQ <93673602+CalMacCQ@users.noreply.github.com>
Date: Tue, 24 Dec 2024 10:30:44 +0000
Subject: [PATCH 17/17] remove unnecessary compilation

---
 .../pytket_qaoa_maxcut_example.ipynb            | 17 +++++++----------
 1 file changed, 7 insertions(+), 10 deletions(-)

diff --git a/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb b/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb
index 84efad7b..2b274a51 100644
--- a/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb
+++ b/docs/examples/algorithms_and_protocols/pytket_qaoa_maxcut_example.ipynb
@@ -353,9 +353,6 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "from pytket import Circuit\n",
-    "\n",
-    "\n",
     "def build_cost_layer(graph: nx.Graph, gamma_val: float) -> Circuit:\n",
     "    circ = Circuit(graph.number_of_nodes())\n",
     "\n",
@@ -476,12 +473,12 @@
     "\n",
     "def eval_qaoa_energy(\n",
     "    backend: Backend,\n",
-    "    compiler_pass: Callable[[Circuit], bool],\n",
     "    guess_mixer_angles: np.array,\n",
     "    guess_cost_angles: np.array,\n",
     "    graph: nx.Graph,\n",
     "    seed: int,\n",
     "    shots: int = 5000,\n",
+    "    compiler_pass: Callable[[Circuit], bool] | None = None,\n",
     ") -> tuple[float, BackendResult]:\n",
     "\n",
     "    # Build Circuit\n",
@@ -491,7 +488,8 @@
     "\n",
     "    # Compile\n",
     "    RemoveBarriers().apply(qaoa_circuit)\n",
-    "    compiler_pass(qaoa_circuit)\n",
+    "    if compiler_pass:\n",
+    "        compiler_pass(qaoa_circuit)\n",
     "\n",
     "    # Execute\n",
     "    result: BackendResult = backend.run_circuit(qaoa_circuit, shots, seed=seed)\n",
@@ -524,12 +522,12 @@
    "source": [
     "def solve_maxcut_instance(\n",
     "    graph: nx.Graph,\n",
-    "    compiler_pass: Callable[[Circuit], bool],\n",
     "    backend: Backend,\n",
     "    iterations: int = 100,\n",
     "    p_value: int = 3,\n",
     "    n_shots: int = 5000,\n",
     "    seed: int = 12345,\n",
+    "    compiler_pass: Callable[[Circuit], bool]| None = None,\n",
     ") -> tuple[BackendResult, np.array, np.array]:\n",
     "\n",
     "    highest_energy = 0\n",
@@ -543,12 +541,12 @@
     "        guess_cost_angles = rng.uniform(0, 1, p_value)\n",
     "        qaoa_energy, result = eval_qaoa_energy(\n",
     "            backend,\n",
-    "            compiler_pass,\n",
     "            guess_mixer_angles,\n",
     "            guess_cost_angles,\n",
     "            seed=seed,\n",
     "            shots=n_shots,\n",
     "            graph=graph,\n",
+    "            compiler_pass=None,\n",
     "        )\n",
     "\n",
     "        if qaoa_energy > highest_energy:\n",
@@ -591,8 +589,7 @@
    "source": [
     "from pytket.extensions.qiskit import AerBackend\n",
     "\n",
-    "backend = AerBackend()\n",
-    "comp = backend.get_compiled_circuit"
+    "backend = AerBackend()"
    ]
   },
   {
@@ -609,7 +606,7 @@
     "%%time\n",
     "qaoa_result, cost_angles, mixer_angles = solve_maxcut_instance(\n",
     "    backend=backend,\n",
-    "    compiler_pass=backend.default_compilation_pass(2).apply,\n",
+    "    compiler_pass=None,\n",
     "    n_shots=5000,\n",
     "    iterations=100,\n",
     "    graph=max_cut_graph,\n",