# File:Qcircuit CNOTfromSQRTSWAP.svg

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Original file(SVG file, nominally 1,618 × 307 pixels, file size: 13 KB)

## Summary

Description
English: Quantum circuit diagram constructing a controlled NOT (CNOT) gate from Sqrt(SWAP) gates and single-qubit operations.
Date
Source Own work
Author Geek3
SVG development
 This vector image was created with LaTeX, postprocessing with pdf2svg, Inkscape and Scour

## The following Mathematica code shows the equality: code

R[x_, y_, z_] := MatrixExp[-I/2 Sum[{x, y, z}[[i]] * PauliMatrix[i], {i, 3}]];
I2 = IdentityMatrix[2];
A_⊗ B_ := KroneckerProduct[A, B];
Z = R[0, 0, Pi];
MRZ = R[0, 0, -Pi/2];
RY = R[0, Pi/2, 0];
MRY = R[0, -Pi/2, 0];
SqrtSwap = MatrixPower[{{1,0,0,0}, {0,0,1,0}, {0,1,0,0}, {0,0,0,1}}, 1/2];

(MRZ⊗(MRY.MRZ)).SqrtSwap.(Z⊗I2).SqrtSwap.(I2⊗RY) // MatrixForm


## Bash

x=Qcircuit_CNOTfromSQRTSWAP;
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


## Using Q-circuit by the following LaTex code: code

\documentclass[border=10pt]{standalone}
\input{Qcircuit} % available on http://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{-RZ} & \qw \\
& \targ & \qw & & & \gate{RY} & \qswap\qwxo{\scalebox{0.7}{$1\hspace{-1pt}/\hspace{-1pt}2$}} & \qw & \qswap\qwxo{\scalebox{0.7}{$1\hspace{-1pt}/\hspace{-1pt}2$}} & \gate{-RZ} & \gate{-RY} & \qw
}}
\end{document}


:::${\displaystyle {\begin{pmatrix}1&0&0&0\\0&1&0&0\\0&0&0&1\\0&0&1&0\end{pmatrix}}}$

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## File history

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Date/TimeThumbnailDimensionsUserComment
current13:33, 19 July 20151,618 × 307 (13 KB)Geek3Qcircuit_CNOTfromSQRTSWAP
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