Merge pull request #35 from marekyggdrasil/issue-26

Issue 26

Author: marekyggdrasil

manuscript.tex

@@ -436,9 +436,14 @@ \subsection{Optimized quantum scheme for Hamming distance calculation}
 The Hamming distance measured in this way is bounded $0 \leq d_{i,j}^H \leq 1$, 
 where  $0$ indicates that $x_i$ are $y_j$ identical and $1$ means they are completely opposite in terms of their pairwise binary coordinates.
 
-In comparison with the circuits for Hamming distance calculations proposed previously \cite{trugenberger2001}, 
-our method allows one to reduce the number of gates in the circuit (at least in $2n$ one-qubit NOT gates)
-and reconstruct all distance matrix in parallel and can be implemented with high fidelity.  
+Currently available quantum platforms are still subject to substantial level of noise and extracting the exact distance from amplitude is still a difficult task.
+Fortunately, for most of algorithms, SOFM included, the information of nearest vectors is sufficient. 
+
+Because of that property, those algorithms fall into a special case category for which, as there is only one input vector considered, the ``Decoding'' stage (Fig.\ref{fig:qcircuit}) can be removed as measurement no longer needs to indicate for which input vector the distance has been measured.
+In this special case scenario the circuit depth complexity is matching with \cite{shuld2014}.
+
+In the general case when multiple input vectors are present in the register, the ``Decoding'' stage still needs to be included leading to larger circuit depth and less attractive complexity in terms of number of controlled gate operations.
+The number of controlled gate operations in this general case of multiple input vectors is matching the number of controlled gate operations in \cite{trugenberger2001}.  
 
 
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