change De Wolf in de Wolf, clarify sentence on classical mechanics

Author: Scinawa

book.bib

@@ -228,7 +228,7 @@ @article{nannicini2019fast
 }
 @article{van2020quantum,
   title        = {Quantum SDP-solvers: Better upper and lower bounds},
-  author       = {Van Apeldoorn, Joran and Gily{\'e}n, Andr{\'a}s and Gribling, Sander and de Wolf, Ronald},
+  author       = {van Apeldoorn, Joran and Gily{\'e}n, Andr{\'a}s and Gribling, Sander and de Wolf, Ronald},
   year         = 2020,
   journal      = {Quantum},
   publisher    = {Verein zur F{\"o}rderung des Open Access Publizierens in den Quantenwissenschaften},
@@ -302,7 +302,7 @@ @article{liu1995ml
 }
 @article{buhrman2001quantum,
   title        = {Quantum fingerprinting},
-  author       = {Buhrman, Harry and Cleve, Richard and Watrous, John and De Wolf, Ronald},
+  author       = {Buhrman, Harry and Cleve, Richard and Watrous, John and de Wolf, Ronald},
   year         = 2001,
   journal      = {Physical Review Letters},
   publisher    = {APS},
@@ -2949,7 +2949,7 @@ @inproceedings{kapoor2016quantum
 }
 @article{DeWolf,
   title        = {Quantum computing: Lecture notes},
-  author       = {De Wolf, Ronald},
+  author       = {de Wolf, Ronald},
   year         = 2019,
   journal      = {arXiv:1907.09415},
 }
@@ -3159,7 +3159,7 @@ @article{Marsden
 }
 @article{Arunachalam2016,
   title        = {{Optimal Quantum Sample Complexity of Learning Algorithms}},
-  author       = {Arunachalam, Srinivasan and De Wolf, Ronald},
+  author       = {Arunachalam, Srinivasan and de Wolf, Ronald},
   year         = 2016,
   arxivid      = {arXiv:1607.00932v2},
 }
@@ -3246,7 +3246,7 @@ @article{Fernando
 }
 @article{DeWolf2008,
   title        = {{A Brief Introduction to Fourier Analysis on the Boolean Cube}},
-  author       = {De Wolf, Ronald},
+  author       = {de Wolf, Ronald},
   year         = 2008,
   pages        = {1--20},
   doi          = {10.4086/toc.gs.2008.001},
@@ -4416,7 +4416,7 @@ @article{Mukund1996
 }
 @article{Cirasella2006,
   title        = {{Classical and Quantum Algorithms for Finding Cycles MSc in Logic}},
-  author       = {Cirasella, Jill and Buhrman, Harry and L{\"{o}}we, Benedikt and De Wolf, Ronald},
+  author       = {Cirasella, Jill and Buhrman, Harry and L{\"{o}}we, Benedikt and de Wolf, Ronald},
   year         = 2006,
 }
 @article{Magniez2005,
@@ -5361,7 +5361,7 @@ @inproceedings{belovs2012span
 }
 @inproceedings{buhrman1999bounds,
   title        = {Bounds for small-error and zero-error quantum algorithms},
-  author       = {Buhrman, Harry and Cleve, Richard and De Wolf, Ronald and Zalka, Christof},
+  author       = {Buhrman, Harry and Cleve, Richard and de Wolf, Ronald and Zalka, Christof},
   year         = 1999,
   booktitle    = {40th Annual Symposium on Foundations of Computer Science (Cat. No. 99CB37039)},
   pages        = {358--368},

intro.Rmd

@@ -33,9 +33,9 @@ there.
 
 When, at the beginning of the 20th century, physicists started to model
 quantum phenomena, they observed that the dynamic of the systems had two
-properties: they observed that the time and space evolution of quantum
-systems is continuous (as in classical mechanics) and reversible (unlike
-the classical world). They decided to formalize this concept as follows.
+properties: the time and space evolution of quantum
+systems is continuous and reversible (as in classical mechanics).
+They decided to formalize this concept as follows.
 First, they decided to model the state of a quantum system at time $p$
 as a function $\psi(p)$, and they decided to model the evolution of
 $\psi(p)$ for time $t$ as an operator $U(t)$ acting on $\psi(p)$s.

sve-based-quantum-algorithms.Rmd

@@ -40,7 +40,7 @@ knitr::include_graphics("algpseudocode/q-factor-score-ratio-estimation.png")
 
 
 
-:::{.theorem #factor_score_estimation, name="Quantum factor score ratio estimation"}
+:::{.theorem #factor_score_estimation name="Quantum factor score ratio estimation"}
  Assume to have quantum access to a matrix $A \in \R^{n \times m}$ and $\sigma_{max} \leq 1$. 
 Let $\gamma, \epsilon$ be precision parameters. There exists a quantum algorithm that, in time $\widetilde{O}\left(\frac{1}{\gamma^2}\frac{\mu(A)}{\epsilon}\right)$, estimates:
 
@@ -60,14 +60,14 @@ Often in data representations, the cumulative sum of the factor score ratios is
 
 However, a slight variation of the algorithm of Theorem \@ref(thm:spectral-norm-estimation) provides a more accurate estimation in less time, given a threshold $\theta$ for the smallest singular value to retain.
 
-:::{.theorem #check_explained_variance, name="Quantum check on the factor score ratios' sum"}
+:::{.theorem #check_explained_variance name="Quantum check on the factor score ratios' sum"}
 Assume to have efficient quantum access to the matrix $A \in \R^{n \times m}$, with singular value decomposition $A = \sum_i\sigma_i u_i v_i^T$. Let $\eta, \epsilon$ be precision parameters and $\theta$ be a threshold for the smallest singular value to consider.
     There exists a quantum algorithm that estimates $p = \frac{\sum_{i: \overline{\sigma}_i \geq \theta} \sigma_i^2}{\sum_j^r \sigma_j^2}$, where $\|\sigma_i - \overline{\sigma}_i\| \leq \epsilon$, to relative error $\eta$ in time $\widetilde{O}\left(\frac{\mu(A)}{\epsilon}\frac{1}{\eta \sqrt{p}}\right)$.
 :::
 
 Moreover, we borrow an observation from  [@kerenidis2017quantumsquares] on Theorem  \@ref(thm:spectral-norm-estimation), to perform a binary search of $\theta$ given the desired sum of factor score ratios.
 
-:::{. theorem #binarysearch-for-threshold name="Quantum binary search for the singular value threshold"}
+:::{.theorem #binarysearch-for-threshold name="Quantum binary search for the singular value threshold"}
 Assume to have quantum access to the matrix $A \in \R^{n \times m}$. Let $p$ be the factor ratios sum to retain. The threshold $\theta$ for the smallest singular value to retain can be estimated to absolute error $\epsilon$ in time $\widetilde{O}\left(\frac{\log(1/\epsilon)\mu(A)}{\epsilon\sqrt{p}}\right)$.
 :::