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English: Quantum circuit diagram constructing a controlled NOT (CNOT) gate from Sqrt(SWAP) gates and single-qubit operations.
Date
Source Own work
Author Geek3
Other versions Qcircuit CNOTfromSQRTSWAP.svg
SVG development
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The SVG code is valid.
 
This vector image was created with LaTeX.
output:
Source code
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Created in LaTeX using Q-circuit by the following code: 
\documentclass[border=10pt]{standalone}
\input{Qcircuit} % available on https://physics.unm.edu/CQuIC/Qcircuit/
\usepackage{graphicx}
\newcommand{\qwxo}[2][-1]{\ar @{-} [#1,0]|*+<4pt,6pt>[Fo]{#2}}
\begin{document}
\scalebox{5}{%
\Qcircuit @C=1.4em @R=1.8em {
	& \ctrl{1} & \qw & \raisebox{-8ex}{=} & & \qw & \qswap & \gate{Z} & \qswap & \qw & \gate{R_Z(-\textstyle\frac\pi2)} & \qw \\
	& \targ & \qw & & & \gate{R_Y(\textstyle\frac\pi2)} & \qswap\qwxo{\scalebox{0.7}{$1\hspace{-1pt}/\hspace{-1pt}2$}} & \qw & \qswap\qwxo{\scalebox{0.7}{$1\hspace{-1pt}/\hspace{-1pt}2$}} & \gate{R_Z(-\textstyle\frac\pi2)} & \gate{R_Y(-\textstyle\frac\pi2)} & \qw
}}
\end{document}
Postprocessing with pdf2svg, Inkscape and Scour: 
x=Qcircuit_CNOTsqrtSWAP2;
pdflatex $x.tex;
pdf2svg $x.pdf $x_.svg;
inkscape --verb=EditSelectAll --verb=SelectionUnGroup --verb=FileVacuum --verb=FileSave --verb=FileClose $x_.svg;
scour -i $x_.svg -o $x.svg --renderer-workaround --remove-metadata --enable-id-stripping --create-groups --enable-viewboxing
The following Mathematica code shows the equality: 
R[x_, y_, z_] := MatrixExp[-I/2 Sum[{x, y, z}[[i]] * PauliMatrix[i], {i, 3}]];
I2 = IdentityMatrix[2];
A_\[CircleTimes] B_ := KroneckerProduct[A, B];
Z = R[0, 0, Pi];
SqrtSwap = MatrixPower[{{1,0,0,0}, {0,0,1,0}, {0,1,0,0}, {0,0,0,1}}, 1/2];
(* Note that the order of operators must be reversed *)
(R[0, 0, -Pi/2]\[CircleTimes](R[0, -Pi/2, 0].R[0, 0, -Pi/2])).SqrtSwap.(Z\[CircleTimes]I2).SqrtSwap.(I2\[CircleTimes]R[0, Pi/2, 0]) // MatrixForm

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Quantum circuit diagram constructing a controlled NOT (CNOT) gate from Sqrt(SWAP) gates and single-qubit operations

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quantum circuit

inception

17 May 2021

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current08:13, 17 May 2021Thumbnail for version as of 08:13, 17 May 20211,878 × 348 (18 KB)Geek3Uploaded own work with UploadWizard

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