Paper VII: Quantum Seed Calculus

Download original file

This is the original TeX manuscript source. Use the paper’s PDF for typeset equations.

Read the typeset paper

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 \node[font=\small,align=center,font=\small] at (2.6,4.7) {$2V$, with $V^*V=I$};
4 \path[draw=black!30,fill=black!8] (1,3.2) rectangle (1.8,4);
5 \node[font=\small,align=center,font=\small] at (1.4,3.6) {$1$};
6 \path[draw=black!30,fill=black!8] (1.8,3.2) rectangle (2.6,4);
7 \node[font=\small,align=center,font=\small] at (2.2,3.6) {$1$};
8 \path[draw=black!30,fill=black!8] (2.6,3.2) rectangle (3.4,4);
9 \node[font=\small,align=center,font=\small] at (3,3.6) {$1$};
10 \path[draw=black!30,fill=black!8] (3.4,3.2) rectangle (4.2,4);
11 \node[font=\small,align=center,font=\small] at (3.8,3.6) {$1$};
12 \path[draw=black!30,fill=black!8] (1,2.4) rectangle (1.8,3.2);
13 \node[font=\small,align=center,font=\small] at (1.4,2.8) {$1$};
14 \path[draw=black!30,fill=black!8] (1.8,2.4) rectangle (2.6,3.2);
15 \node[font=\small,align=center,font=\small] at (2.2,2.8) {$- i$};
16 \path[draw=black!30,fill=black!8] (2.6,2.4) rectangle (3.4,3.2);
17 \node[font=\small,align=center,font=\small] at (3,2.8) {$-1$};
18 \path[draw=black!30,fill=black!8] (3.4,2.4) rectangle (4.2,3.2);
19 \node[font=\small,align=center,font=\small] at (3.8,2.8) {$i$};
20 \path[draw=black!30,fill=black!8] (1,1.6) rectangle (1.8,2.4);
21 \node[font=\small,align=center,font=\small] at (1.4,2) {$1$};
22 \path[draw=black!30,fill=black!8] (1.8,1.6) rectangle (2.6,2.4);
23 \node[font=\small,align=center,font=\small] at (2.2,2) {$-1$};
24 \path[draw=black!30,fill=black!8] (2.6,1.6) rectangle (3.4,2.4);
25 \node[font=\small,align=center,font=\small] at (3,2) {$1$};
26 \path[draw=black!30,fill=black!8] (3.4,1.6) rectangle (4.2,2.4);
27 \node[font=\small,align=center,font=\small] at (3.8,2) {$-1$};
28 \path[draw=black!30,fill=black!8] (1,0.8) rectangle (1.8,1.6);
29 \node[font=\small,align=center,font=\small] at (1.4,1.2) {$1$};
30 \path[draw=black!30,fill=black!8] (1.8,0.8) rectangle (2.6,1.6);
31 \node[font=\small,align=center,font=\small] at (2.2,1.2) {$i$};
32 \path[draw=black!30,fill=black!8] (2.6,0.8) rectangle (3.4,1.6);
33 \node[font=\small,align=center,font=\small] at (3,1.2) {$-1$};
34 \path[draw=black!30,fill=black!8] (3.4,0.8) rectangle (4.2,1.6);
35 \node[font=\small,align=center,font=\small] at (3.8,1.2) {$- i$};
36 \node[font=\small,align=center,anchor=east,font=\scriptsize] at (0.85,3.6) {site 0};
37 \node[font=\small,align=center,anchor=east,font=\scriptsize] at (0.85,2.8) {site 1};
38 \node[font=\small,align=center,anchor=east,font=\scriptsize] at (0.85,2) {site 2};
39 \node[font=\small,align=center,anchor=east,font=\scriptsize] at (0.85,1.2) {site 3};
40 \node[font=\small,align=center,font=\scriptsize] at (1.4,4.23) {$j=0$};
41 \node[font=\small,align=center,font=\scriptsize] at (2.2,4.23) {$j=1$};
42 \node[font=\small,align=center,font=\scriptsize] at (3,4.23) {$j=2$};
43 \node[font=\small,align=center,font=\scriptsize] at (3.8,4.23) {$j=3$};
44 \node[font=\small,align=center,font=\small] at (8.05,3.8) {$S v_0=1v_0$};
45 \node[font=\small,align=center,font=\small] at (11.85,3.8) {$P_0=v_0v_0^*$};
46 \node[font=\small,align=center,font=\small] at (8.05,2.95) {$S v_1=iv_1$};
47 \node[font=\small,align=center,font=\small] at (11.85,2.95) {$P_1=v_1v_1^*$};
48 \node[font=\small,align=center,font=\small] at (8.05,2.1) {$S v_2=-1v_2$};
49 \node[font=\small,align=center,font=\small] at (11.85,2.1) {$P_2=v_2v_2^*$};
50 \node[font=\small,align=center,font=\small] at (8.05,1.25) {$S v_3=- iv_3$};
51 \node[font=\small,align=center,font=\small] at (11.85,1.25) {$P_3=v_3v_3^*$};
52 \node[font=\small,align=center,font=\scriptsize] at (8.8,0.12) {Each column has four entries of magnitude $1/2$.};
53 \end{tikzpicture}

Back to source controls

Back to Paper VII: Quantum Seed Calculus