File:Quantum Fourier transform on n qubits.svg

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Summary

Description
English: Quantum Fourier transform on n qubits.
Source Created in LaTeX using Q-circuit. Source code below.
Author Self
\documentclass[10pt]{article}

\usepackage[hang,small,bf]{caption}    % fancy captions

\usepackage{tikz}	
\usetikzlibrary{backgrounds,fit,decorations.pathreplacing}  % TikZ libraries

\newcommand{\ket}[1]{\ensuremath{\left|#1\right\rangle}} % Dirac Kets
\begin{document}

\begin{figure}[h]  
\centerline{     
\begin{tikzpicture}[thick]     
%     
% `operator' will only be used by Hadamard (H) gates here.     
% `phase' is used for controlled phase gates (dots).     
% `surround' is used for the background box.     
\tikzstyle{operator} = [draw,fill=white,minimum size=1.5em]      
\tikzstyle{phase} = [fill,shape=circle,minimum size=5pt,inner sep=0pt]  
%\tikzstyle{surround} = [fill=red!10,thick,draw=white,rounded corners=2mm] 	
\tikzstyle{phase1} = [draw=black,shape=circle,minimum size=8pt,inner sep=0pt]  
\tikzstyle{phase3} = [fill,shape=circle,minimum size=0pt,inner sep=0pt]  
%
% columna     
\node at (-2,0) (q1) {\ket{x_{1}}};     
\node at (-2,-1) (q2) {\ket{x_{2}}}; 
\node at (-2,-2) (q3) {\vdots}; 
\node at (-2,-3) (q5) {\ket{x_{n-1}}};     
\node at (-2,-4) (q6) {\ket{x_{n}}}; 
%        
% Column 1 
\node[operator] at (-1,0) (q7) {H} edge [-] (q1);     
% Columna 2
\node at (0,-2) (q4) {\vdots};
\node[operator] at (0,0) (q8) {$R_{2}$} edge [-] (q7);
\node[phase] at (0,-1) (q9) {} edge [-] (q8) edge [-] (q2);
%
%Columna 3
\node at (1,0) (q10) {\dots} edge [-] (q8); 
\node at (1,-1) (q11) {\dots} edge [-] (q9); 
%
%          
%    
% Column 4  
\node[operator] at (2,0) (q12) {$R_{n-1}$} edge [-] (q10);
\node[phase] at (2,-3) (q13) {} edge [-] (q12) edge [-] (q5);
\node[phase3] at (2,-1) (q14) {} edge [-] (q11);  
%Columna 5
\node[operator] at (3.2,0) (q15) {$R_{n}$} edge [-] (q12);
\node[phase] at (3.2,-4) (q16) {} edge [-] (q15) edge [-] (q6);
%Columna 6
\node[operator] at (4,-1) (q17) {H} edge [-] (q11);
%columna 7
\node at (5,-1) (q18) {\dots} edge [-] (q17); 
%columna 8
\node[operator] at (6,-1) (q19) {$R_{n-2}$} edge [-] (q18);
\node[phase] at (6,-3) (q20) {} edge [-] (q19) edge [-] (q13);
%columna 9/10
\node[operator] at (7.5,-1) (q21) {$R_{n-1}$} edge [-] (q19);
\node[phase] at (7.5,-4) (q22) {} edge [-] (q21) edge [-] (q16);
%columna 11
\node at (9,-1) (q23) {\dots} edge [-] (q21); 
\node at (9,-3) (q24) {\dots} edge [-] (q20);
\node at (9,-4) (q25) {\dots} edge [-] (q22);
%columna 12
\node[operator] at (10,-3) (q26) {H} edge [-] (q24);
% columna 13
\node[operator] at (11,-3) (q27) {$R_{2}$} edge [-] (q26);
\node[phase] at (11,-4) (q28) {} edge [-] (q27) edge [-] (q25);
%columna 14
\node[operator] at (12,-4) (q29) {H} edge [-] (q28);
%columna 15
\node at (14.2,0) (q31) {\ket{0}+$e^{2\pi i0.x_{1}x_{2}..x_{n}}$\ket{1}} edge [-] (q15);     
\node at (14.2,-1) (q32) {\ket{0}+$e^{2\pi i0.x_{2}..x_{n}}$\ket{1}} edge [-] (q23); 
\node at (14.2,-2) (q33) {\vdots}; 
\node at (14.2,-3) (q35) {\ket{0}+$e^{2\pi i0.x_{n-1}..x_{n}}$\ket{1}} edge [-] (q27);     
\node at (14.2,-4) (q36) {\ket{0}+$e^{2\pi i0.x_{n}}$\ket{1}} edge [-] (q29);
%
\end{tikzpicture}  
} 
\end{figure}
\end{document}

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w:en:Creative Commons
attribution
This file is licensed under the Creative Commons Attribution 3.0 Unported license.
You are free:
  • to share – to copy, distribute and transmit the work
  • to remix – to adapt the work
Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
You may select the license of your choice.

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Date/TimeThumbnailDimensionsUserComment
current21:53, 28 March 2011Thumbnail for version as of 21:53, 28 March 2011563 × 200 (76 KB)Bender2k14Using the undocumented pureghost command of Q-circuit, removed an unnecessary wire.
04:10, 11 March 2011Thumbnail for version as of 04:10, 11 March 2011562 × 200 (84 KB)Bender2k14{{Information |Description ={{en|1=Quantum Fourier transform on ''n'' qubits.}} |Source =Created in LaTeX using [http://www.cquic.org/Qcircuit/ Q-circuit]. Source code below. |Author =Self |Date = |Permission = |other_vers
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