File:Qcircuit CNOTfromSQRTSWAP.svg
Summary
Category:Commons:Maint:Igen:T
| 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 |
| Other versions | Qcircuit CNOTsqrtSWAP2.svg |
| SVG development | |
| Source code | The following Mathematica code shows the equality: codeR[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
Bashx=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}
|
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