Paper VII: Quantum Seed Calculus

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1 \begin{tikzpicture}[x=1cm,y=1cm,>=Stealth,line cap=round,line join=round]
2 \path[use as bounding box] (0,-.6) rectangle (14,4.8);
3 \draw[black!55,line width=.6pt] (1,0.65) -- (4.35,0.65);
4 \draw[black!55,line width=.6pt] (1,0.65) -- (1,3.1);
5 \draw[dashed,black!55,line width=.6pt] (1,0.65) -- (2.65,1.6);
6 \draw[black!55,line width=.6pt] (4.35,0.65) -- (4.35,3.1);
7 \draw[dashed,black!55,line width=.6pt] (4.35,0.65) -- (6,1.6);
8 \draw[black!55,line width=.6pt] (1,3.1) -- (4.35,3.1);
9 \draw[dashed,black!55,line width=.6pt] (1,3.1) -- (2.65,4.05);
10 \draw[dashed,black!55,line width=.6pt] (4.35,3.1) -- (6,4.05);
11 \draw[black!55,line width=.6pt] (2.65,1.6) -- (6,1.6);
12 \draw[black!55,line width=.6pt] (2.65,1.6) -- (2.65,4.05);
13 \draw[black!55,line width=.6pt] (6,1.6) -- (6,4.05);
14 \draw[black!55,line width=.6pt] (2.65,4.05) -- (6,4.05);
15 \path[draw,fill=white] (0.53,0.35) rectangle (1.47,0.95);
16 \node[font=\small,align=center] at (1,0.65) {$\ket{000}$};
17 \path[draw,fill=white] (3.88,0.35) rectangle (4.82,0.95);
18 \node[font=\small,align=center] at (4.35,0.65) {$\ket{001}$};
19 \path[draw,fill=white] (0.53,2.8) rectangle (1.47,3.4);
20 \node[font=\small,align=center] at (1,3.1) {$\ket{010}$};
21 \path[draw,fill=white] (3.88,2.8) rectangle (4.82,3.4);
22 \node[font=\small,align=center] at (4.35,3.1) {$\ket{011}$};
23 \path[draw,fill=white] (2.18,1.3) rectangle (3.12,1.9);
24 \node[font=\small,align=center] at (2.65,1.6) {$\ket{100}$};
25 \path[draw,fill=white] (5.53,1.3) rectangle (6.47,1.9);
26 \node[font=\small,align=center] at (6,1.6) {$\ket{101}$};
27 \path[draw,fill=white] (2.18,3.75) rectangle (3.12,4.35);
28 \node[font=\small,align=center] at (2.65,4.05) {$\ket{110}$};
29 \path[draw,fill=white] (5.53,3.75) rectangle (6.47,4.35);
30 \node[font=\small,align=center] at (6,4.05) {$\ket{111}$};
31 \node[font=\small,align=center,font=\small] at (10.15,4.1) {Three actual words};
32 \node[font=\small,align=center,font=\small] at (10.15,3.1) {$W_{101}=X_1X_3$};
33 \node[font=\small,align=center,font=\small] at (10.15,2.2) {$W_{011}=X_2X_3$};
34 \node[font=\small,align=center,font=\small] at (10.15,1.3) {$W_{110}=X_1X_2$};
35 \node[font=\small,align=center,font=\small] at (6.65,0.1) {$\dim\Span\{W_a\ket{000}\}=8$};
36 \end{tikzpicture}

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