├── .gitattributes ├── .gitignore ├── LICENSE ├── README.md ├── desktop.ini ├── figures ├── 1qcirc-k0.tikz ├── 1qcirc-k1.tikz ├── Bell_basis_states.tikz ├── Bellmaps.tikz ├── Bellstate_circuitmodel.tikz ├── Bellstate_measAlice.tikz ├── Bellstate_zx.tikz ├── Bellstate_zx_green.tikz ├── Bellstate_zx_red.tikz ├── Bellstate_zx_x.tikz ├── Bellstate_zx_z.tikz ├── Belltest2_zx01.tikz ├── Belltest2_zx10.tikz ├── Belltest2_zx11.tikz ├── Belltest_zx.tikz ├── Belltest_zx01.tikz ├── Belltest_zx10.tikz ├── Belltest_zx11.tikz ├── Belltestzxposter.tikz ├── H_rule.tikz ├── H_rule_other.tikz ├── Igate.tikz ├── X_spider_fusion.tikz ├── Z_spider_fusion.tikz ├── avocadogrilledcheesesandwich.tikz ├── bloch+-.tikz ├── bloch+-wrt01.tikz ├── bloch+.tikz ├── bloch+i-i.tikz ├── bloch-.tikz ├── bloch0.tikz ├── bloch01.tikz ├── bloch1.tikz ├── blochh.tikz ├── blochrx.tikz ├── blochrxyz.tikz ├── blochry.tikz ├── blochrz.tikz ├── blochrzrotate.tikz ├── blochsphere.tikz ├── blochxyz.tikz ├── blochxyzstates.tikz ├── bra+i.tikz ├── bra-i.tikz ├── bra0.tikz ├── bra1.tikz ├── braket++.tikz ├── braket++unnorm.tikz ├── braket+-.tikz ├── braket-+.tikz ├── braket--.tikz ├── braket0+.tikz ├── braket0-.tikz ├── braket00.tikz ├── braket01.tikz ├── braket1+.tikz ├── braket1-.tikz ├── braket10.tikz ├── braket11.tikz ├── cache │ ├── qiskit+zx-figure0.dpth │ ├── qiskit+zx-figure0.md5 │ └── qiskit+zx-figure0.pdf ├── circuitcolorchange.tikz ├── circuitcommuteHX.tikz ├── classical_logic_gates.tikz ├── conjugateandtransposemaps.tikz ├── conjugateandtransposestates.tikz ├── cx_circuitmodel.tikz ├── cx_circuitmodel2.tikz ├── deformation-example.tikz ├── demorganslaw1.tikz ├── demorganslaw2.tikz ├── jamsandwich.tikz ├── ket+.tikz ├── ket+i.tikz ├── ket+iconj.tikz ├── ket+itranspose.tikz ├── ket+unnorm.tikz ├── ket+unnormsuperposition.tikz ├── ket-.tikz ├── ket-i.tikz ├── ket-iconj.tikz ├── ket-itranspose.tikz ├── ket.tikz ├── ket0.tikz ├── ket0switch.tikz ├── ket1.tikz ├── ket1switch.tikz ├── ket_doubled.tikz ├── ketpsi.tikz ├── ketv.tikz ├── latitude.tikz ├── lightbulb_simp.tikz ├── lightbulb_test00.tikz ├── lightbulb_test01.tikz ├── lightbulb_test10.tikz ├── lightbulb_test11.tikz ├── longitude.tikz ├── map_around_cup_transpose.tikz ├── nand.tikz ├── nkets.tikz ├── nnorn.tikz ├── nnorn_simp1.tikz ├── nnorn_simp2.tikz ├── nnorn_simp3.tikz ├── nor.tikz ├── notnot.tikz ├── ntoasts.tikz ├── oneket.tikz ├── onetoast.tikz ├── qubitordering_circuitmodel.tikz ├── slide_map_around_cup.tikz ├── slide_state_around_cap.tikz ├── slide_state_around_cup.tikz ├── sphericalcoordinates.tikz ├── state-map-duality_gen.tikz ├── state-map-duality_map.tikz ├── state-map-duality_state.tikz ├── sterngerlachzx.tikz ├── sterngerlachzxz.tikz ├── sterngerlachzz.tikz ├── switch_off.tikz ├── switch_on.tikz ├── switch_process.tikz ├── teaorcookies.tikz ├── toastsandwich.tikz ├── transpose_map_def.tikz ├── transpose_maps.tikz ├── twok0s.tikz ├── twokets.tikz ├── twotoasts.tikz ├── unitcircle+-.tikz ├── unitcircle01+-.tikz ├── unitcircle01.tikz ├── unitcirclecomplexinbloch.tikz ├── unitcirclehopposite.tikz ├── unitcirclehreflect.tikz ├── unitcircleinbloch.tikz ├── unitcircletriangle.tikz ├── unitcircletrinoangle.tikz ├── unitcirclex.tikz ├── unitcirclexex.tikz ├── unitcirclez.tikz ├── unitcirclezex.tikz ├── x_circuitmodel.tikz ├── x_circuitmodel2.tikz ├── yank.tikz ├── yank2.tikz ├── yankBell.tikz ├── yankBell_zx01.tikz ├── yankBell_zx10.tikz ├── yankBell_zx11.tikz ├── yankZ.tikz ├── zxCX.tikz ├── zxCXXphase.tikz ├── zxCXZphase.tikz ├── zxCXbendy.tikz ├── zxCXcopy.tikz ├── zxCXcopy0.tikz ├── zxCXcopy1.tikz ├── zxCXcopymatch.tikz ├── zxCXcopyz.tikz ├── zxCXsum.tikz ├── zxH.tikz ├── zxHEuler1.tikz ├── zxHEuler2.tikz ├── zxHH.tikz ├── zxHedge.tikz ├── zxS.tikz ├── zxT.tikz ├── zxX.tikz ├── zxXI.tikz ├── zxXfusion1q.tikz ├── zxXfusion1qff.tikz ├── zxXfusion1qft.tikz ├── zxXfusion1qtf.tikz ├── zxXfusion1qtt.tikz ├── zxXk0.tikz ├── zxXk1.tikz ├── zxXphase.tikz ├── zxZ.tikz ├── zxZI.tikz ├── zxZXI.tikz ├── zxZfusion1qff.tikz ├── zxZfusion1qfffttf.tikz ├── zxZfusion1qft.tikz ├── zxZfusion1qstate.tikz ├── zxZfusion1qstatetest.tikz ├── zxZfusion1qtest.tikz ├── zxZfusion1qtf.tikz ├── zxZfusion1qtt.tikz ├── zxZk+.tikz ├── zxZk-.tikz ├── zxZphase.tikz ├── zxbialgebracopy.tikz ├── zxbialgebracopyapi.tikz ├── zxbialgebracopyapiT.tikz ├── zxbialgebracopyapih.tikz ├── zxbialgebracopyapioppcolor.tikz ├── zxbialgebracopyapioppcolorT.tikz ├── zxbialgebracopypi.tikz ├── zxcolorchange.tikz ├── zxcommuteHX.tikz ├── zxcopybendy.tikz ├── zxk+.tikz ├── zxk-.tikz ├── zxk0.tikz ├── zxk1.tikz ├── zxmatchsum.tikz └── zxothercolorchange.tikz ├── images ├── HelloWorld-2_IBMQuantumLab.PNG ├── HelloWorld-4_IBMQuantumLab.PNG ├── HelloWorld_IBMQuantumLab.PNG ├── HelloWorld_run_IBMQuantumLab.PNG ├── Launcher_IBMQuantumLab.PNG ├── Measure_IBMQuantumComposer.PNG ├── NewCircuit_IBMQuantumComposer.PNG ├── ket1_IBMQuantumComposer.PNG └── rainbowtsmc.jpg ├── preamble.tex ├── qiskit+zx-blx.bib ├── qiskit+zx.auxlock ├── qiskit+zx.bbl ├── qiskit+zx.bcf ├── qiskit+zx.bib ├── qiskit+zx.blg ├── qiskit+zx.out ├── qiskit+zx.pdf ├── qiskit+zx.run.xml ├── qiskit+zx.tex ├── qiskit+zx.toc ├── qseec22-poster.pdf ├── tikzit.sty ├── zx.tikzdefs └── zx.tikzstyles /.gitattributes: -------------------------------------------------------------------------------- 1 | *.pdf filter=lfs diff=lfs merge=lfs -text 2 | *.jpg filter=lfs diff=lfs merge=lfs -text 3 | *.PNG filter=lfs diff=lfs merge=lfs -text 4 | *.synctex(busy) filter=lfs diff=lfs merge=lfs -text 5 | -------------------------------------------------------------------------------- /.gitignore: -------------------------------------------------------------------------------- 1 | *.log 2 | *.synctex.gz 3 | *.aux 4 | images/ -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Learning QC with ZX 2 | Learning quantum computing concepts via ZX 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[style=none] (8) at (-1.75, -0.75) {$\ket{q_t}$}; 11 | \end{pgfonlayer} 12 | \begin{pgfonlayer}{edgelayer} 13 | \draw (0) to (1); 14 | \draw [style=simple] (5.center) to (0); 15 | \draw [style=simple] (0) to (3.center); 16 | \draw [style=simple] (6.center) to (1); 17 | \draw [style=simple] (1) to (4.center); 18 | \end{pgfonlayer} 19 | \end{tikzpicture} 20 | -------------------------------------------------------------------------------- /figures/deformation-example.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=none] (21) at (0, 0) {=}; 4 | \node [style=none] (22) at (-6.25, 2.25) {}; 5 | \node [style=none] (23) at (-6.25, -0.25) {}; 6 | \node [style=none] (24) at (-6.25, -2.5) {}; 7 | \node [style=none] (25) at (-1.5, 1.25) {}; 8 | \node [style=none] (26) at (-1.5, -1) {}; 9 | \node [style=Z phase dot] (27) at (-4.75, 2.25) {$\pi$}; 10 | \node [style=X dot] (28) at (-2.75, -1) {}; 11 | \node [style=Z dot] (29) at (-4.5, 0.5) {}; 12 | \node [style=X phase dot] (30) at (-2.75, 1.25) {$\frac\pi2$}; 13 | \node [style=Z phase dot] (31) at (-3.5, -2) {$\frac\pi4$}; 14 | \node [style=X phase dot] (32) at (-2, -0.25) {-$\frac\pi2$}; 15 | \node [style=X phase dot] (44) at (-3.5, -0.5) {$\pi$}; 16 | \node [style=none] (58) at (1.5, 2.25) {}; 17 | \node [style=none] (59) at (1.5, -0.25) {}; 18 | \node [style=none] (60) at (1.5, -2.5) {}; 19 | \node [style=none] (61) at (7.5, 1.25) {}; 20 | \node [style=none] (62) at (7.25, -1) {}; 21 | \node [style=Z phase dot] (63) at (2.25, 1.5) {$\pi$}; 22 | \node [style=X dot] (64) at (5, -1) {}; 23 | \node [style=Z dot] (65) at (4, 2.25) {}; 24 | \node [style=X phase dot] (66) at (3.5, -0.5) {$\frac\pi2$}; 25 | \node [style=Z phase dot] (67) at (5.75, -0.25) {$\frac\pi4$}; 26 | \node [style=X phase dot] (68) at (2, -1.25) {-$\frac\pi2$}; 27 | \node [style=X phase dot] (69) at (4.75, 1) {$\pi$}; 28 | \node [style=none] (70) at (6, 0.75) {}; 29 | \end{pgfonlayer} 30 | \begin{pgfonlayer}{edgelayer} 31 | \draw (28) to (26.center); 32 | \draw (22.center) to (27); 33 | \draw (27) to (29); 34 | \draw [in=225, out=0] (23.center) to (29); 35 | \draw (30) to (25.center); 36 | \draw [in=0, out=-150, looseness=0.75] (30) to (24.center); 37 | \draw (30) to (29); 38 | \draw (31) to (28); 39 | \draw (29) to (44); 40 | \draw (44) to (28); 41 | \draw (64) to (62.center); 42 | \draw [in=15, out=0, looseness=2.75] (58.center) to (63); 43 | \draw [in=-120, out=-180, looseness=3.50] (63) to (65); 44 | \draw [in=-180, out=0, looseness=0.75] (59.center) to (65); 45 | \draw [in=180, out=0, looseness=0.75] (66) to (61.center); 46 | \draw [bend left] (66) to (60.center); 47 | \draw (66) to (65); 48 | \draw [in=90, out=-60, looseness=0.75] (65) to (69); 49 | \draw [in=120, out=-90, looseness=0.75] (69) to (64); 50 | \draw [in=180, out=165, looseness=1.75] (64) to (70.center); 51 | \draw [in=0, out=0, looseness=2.75] (70.center) to (67); 52 | \end{pgfonlayer} 53 | \end{tikzpicture} 54 | -------------------------------------------------------------------------------- /figures/ket+.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=none] (0) at (11.75, 0) {$\coloneqq$}; 4 | \node [style=none] (1) at (10.25, 0) {\large$\ket{+}$}; 5 | \node [style=none] (2) at (5.75, -0.5) {}; 6 | \node [style=none] (3) at (7, -0.5) {}; 7 | \node [style=none] (4) at (5.75, -2) {}; 8 | \node [style=none] (5) at (5.75, -0.5) {}; 9 | \node [style=none] (6) at (8.5, 0) {$\coloneqq$}; 10 | \node [style=none] (7) at (5.75, 1) {}; 11 | \node [style=none] (8) at (5.75, -1) {\large$+$}; 12 | \node [style=none] (9) at (13.75, 0) {$\large{\frac{1}{\sqrt{2}}}\begin{bmatrix}1\\ 1\end{bmatrix}$}; 13 | \node [style=none] (10) at (4.5, -0.5) {}; 14 | \node [style=none] (11) at (5.75, 1.75) {}; 15 | \end{pgfonlayer} 16 | \begin{pgfonlayer}{edgelayer} 17 | \draw (4.center) to (3.center); 18 | \draw (3.center) to (2.center); 19 | \draw [style=simple] (7.center) to (5.center); 20 | \draw [style=simple] (5.center) to (10.center); 21 | \draw [style=simple] (10.center) to (4.center); 22 | \end{pgfonlayer} 23 | \end{tikzpicture} 24 | -------------------------------------------------------------------------------- /figures/ket+i.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=none] (0) at (11.75, 0) {$\coloneqq$}; 4 | \node [style=none] (1) at (10.25, 0) {\large$\ket{+i}$}; 5 | \node [style=none] (3) at (7, -0.5) {}; 6 | \node [style=none] (4) at (5.75, -2) {}; 7 | \node [style=none] (5) at (5.75, -0.5) {}; 8 | \node [style=none] (6) at (8.5, 0) {$\coloneqq$}; 9 | \node [style=none] (7) at (5.75, 1) {}; 10 | \node [style=none] (8) at (5.75, -1) {\large$+i$}; 11 | \node [style=none] (9) at (14, 0) {$\large{\frac{1}{\sqrt{2}}}\begin{bmatrix}1\\ i\end{bmatrix}$}; 12 | \node [style=none] (11) at (5.75, 1.75) {}; 13 | \node [style=none] (13) at (7, -0.5) {}; 14 | \node [style=none] (14) at (5.75, -2) {}; 15 | \node [style=none] (15) at (5.75, -0.5) {}; 16 | \node [style=none] (17) at (5.125, -0.5) {}; 17 | \node [style=none] (18) at (5.125, -1.25) {}; 18 | \end{pgfonlayer} 19 | \begin{pgfonlayer}{edgelayer} 20 | \draw (4.center) to (3.center); 21 | \draw [style=simple] (7.center) to (5.center); 22 | \draw (14.center) to (13.center); 23 | \draw [style=simple] (15.center) to (17.center); 24 | \draw [style=simple] (17.center) to (18.center); 25 | \draw [style=simple] (18.center) to (14.center); 26 | \draw (3.center) to (5.center); 27 | \draw (13.center) to (15.center); 28 | \end{pgfonlayer} 29 | \end{tikzpicture} 30 | -------------------------------------------------------------------------------- /figures/ket+iconj.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=none] (0) at (12.25, 0) {$\coloneqq$}; 4 | \node [style=none] (1) at (10.25, 0) {\large$\left(\ket{+i}\right)^*$}; 5 | \node [style=none] (5) at (8.5, 0) {$\coloneqq$}; 6 | \node [style=none] (8) at (16.5, 0) {$\left(\large{\frac{1}{\sqrt{2}}}\begin{bmatrix}1\\ i\end{bmatrix}\right)^* = \large{\frac{1}{\sqrt{2}}}\begin{bmatrix}1\\ -i\end{bmatrix}$}; 7 | \node [style=none] (37) at (4.5, -0.5) {}; 8 | \node [style=none] (38) at (5.75, -2) {}; 9 | \node [style=none] (39) at (5.75, -0.5) {}; 10 | \node [style=none] (40) at (5.75, 1) {}; 11 | \node [style=none] (41) at (5.75, -1) {\large$+i$}; 12 | \node [style=none] (42) at (5.75, 1.75) {}; 13 | \node [style=none] (43) at (4.5, -0.5) {}; 14 | \node [style=none] (44) at (5.75, -2) {}; 15 | \node [style=none] (45) at (5.75, -0.5) {}; 16 | \node [style=none] (46) at (6.375, -0.5) {}; 17 | \node [style=none] (47) at (6.375, -1.25) {}; 18 | \end{pgfonlayer} 19 | \begin{pgfonlayer}{edgelayer} 20 | \draw (38.center) to (37.center); 21 | \draw [style=simple] (40.center) to (39.center); 22 | \draw (44.center) to (43.center); 23 | \draw [style=simple] (45.center) to (46.center); 24 | \draw [style=simple] (46.center) to (47.center); 25 | \draw [style=simple] (47.center) to (44.center); 26 | \draw (37.center) to (39.center); 27 | \draw (43.center) to (45.center); 28 | \end{pgfonlayer} 29 | \end{tikzpicture} 30 | -------------------------------------------------------------------------------- /figures/ket+itranspose.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=none] (0) at (12.25, 0) {$\coloneqq$}; 4 | \node [style=none] (1) at (10.25, 0) {\large$\left(\ket{+i}\right)^{\transpose}$}; 5 | \node [style=none] (5) at (8.5, 0) {$\coloneqq$}; 6 | \node [style=none] (8) at (18, 0) {$\left(\large{\frac{1}{\sqrt{2}}}\begin{bmatrix}1\\ i\end{bmatrix}\right)^{\transpose} = \large{\frac{1}{\sqrt{2}}}\begin{bmatrix}1 & i\end{bmatrix}$}; 7 | \node [style=none] (37) at (4.5, 0.25) {}; 8 | \node [style=none] (38) at (5.75, 1.75) {}; 9 | \node [style=none] (39) at (5.75, 0.25) {}; 10 | \node [style=none] (40) at (5.75, -1.25) {}; 11 | \node [style=none] (41) at (5.75, 0.75) {\large$+i$}; 12 | \node [style=none] (42) at (5.75, -2) {}; 13 | \node [style=none] (43) at (4.5, 0.25) {}; 14 | \node [style=none] (44) at (5.75, 1.75) {}; 15 | \node [style=none] (45) at (5.75, 0.25) {}; 16 | \node [style=none] (46) at (6.375, 0.25) {}; 17 | \node [style=none] (47) at (6.375, 1) {}; 18 | \end{pgfonlayer} 19 | \begin{pgfonlayer}{edgelayer} 20 | \draw (38.center) to (37.center); 21 | \draw [style=simple] (40.center) to (39.center); 22 | \draw (44.center) to (43.center); 23 | \draw [style=simple] (45.center) to (46.center); 24 | \draw [style=simple] (46.center) to (47.center); 25 | \draw [style=simple] (47.center) to (44.center); 26 | \draw (37.center) to (39.center); 27 | \draw (43.center) to (45.center); 28 | \end{pgfonlayer} 29 | \end{tikzpicture} 30 | -------------------------------------------------------------------------------- /figures/ket+unnorm.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=none] (0) at (11.75, 0) {$\coloneqq$}; 4 | \node [style=none] (1) at (10.25, 0) {\large$\ket{+}$}; 5 | \node [style=none] (2) at (5.75, -0.5) {}; 6 | \node [style=none] (3) at (7, -0.5) {}; 7 | \node [style=none] (4) at (5.75, -2) {}; 8 | \node [style=none] (5) at (5.75, -0.5) {}; 9 | \node [style=none] (6) at (8.5, 0) {$\coloneqq$}; 10 | \node [style=none] (7) at (5.75, 1) {}; 11 | \node [style=none] (8) at (5.75, -1) {\large$+$}; 12 | \node [style=none] (9) at (13.75, 0) {$\begin{bmatrix}1\\ 1\end{bmatrix}$}; 13 | \node [style=none] (10) at (4.5, -0.5) {}; 14 | \node [style=none] (11) at (5.75, 1.75) {}; 15 | \end{pgfonlayer} 16 | \begin{pgfonlayer}{edgelayer} 17 | \draw (4.center) to (3.center); 18 | \draw (3.center) to (2.center); 19 | \draw [style=simple] (7.center) to (5.center); 20 | \draw [style=simple] (5.center) to (10.center); 21 | \draw [style=simple] (10.center) to (4.center); 22 | \end{pgfonlayer} 23 | \end{tikzpicture} 24 | -------------------------------------------------------------------------------- /figures/ket+unnormsuperposition.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=none] (2) at (5.75, -0.5) {}; 4 | \node [style=none] (3) at (7, -0.5) {}; 5 | \node [style=none] (4) at (5.75, -2) {}; 6 | \node [style=none] (5) at (5.75, -0.5) {}; 7 | \node [style=none] (6) at (8.5, 0) {$=$}; 8 | \node [style=none] (7) at (5.75, 1) {}; 9 | \node [style=none] (8) at (5.75, -1) {\large$+$}; 10 | \node [style=none] (10) at (4.5, -0.5) {}; 11 | \node [style=none] (11) at (5.75, 1.75) {}; 12 | \node [style=none] (29) at (8.5, -7) {$=$}; 13 | \node [style=none] (30) at (11, -7.5) {}; 14 | \node [style=none] (31) at (12.25, -7.5) {}; 15 | \node [style=none] (32) at (11, -9) {}; 16 | \node [style=none] (33) at (11, -7.5) {}; 17 | \node [style=none] (34) at (11, -6) {}; 18 | \node [style=none] (35) at (11, -8) {\large$0$}; 19 | \node [style=none] (36) at (9.75, -7.5) {}; 20 | \node [style=none] (37) at (11, -5.25) {}; 21 | \node [style=none] (38) at (13.75, -7) {$+$}; 22 | \node [style=none] (39) at (16.25, -7.5) {}; 23 | \node [style=none] (40) at (17.5, -7.5) {}; 24 | \node [style=none] (41) at (16.25, -9) {}; 25 | \node [style=none] (42) at (16.25, -7.5) {}; 26 | \node [style=none] (43) at (16.25, -6) {}; 27 | \node [style=none] (44) at (16.25, -8) {\large$1$}; 28 | \node [style=none] (45) at (15, -7.5) {}; 29 | \node [style=none] (46) at (16.25, -5.25) {}; 30 | \node [style=none] (47) at (13.75, 0) {$\begin{bmatrix}1\\ 1\end{bmatrix}$}; 31 | \node [style=none] (48) at (8.5, -3.5) {$=$}; 32 | \node [style=none] (49) at (13.75, -3.5) {$+$}; 33 | \node [style=none] (50) at (11, -3.5) {$\begin{bmatrix}1\\ 0\end{bmatrix}$}; 34 | \node [style=none] (51) at (16.25, -3.5) {$\begin{bmatrix}0\\ 1\end{bmatrix}$}; 35 | \end{pgfonlayer} 36 | \begin{pgfonlayer}{edgelayer} 37 | \draw (4.center) to (3.center); 38 | \draw (3.center) to (2.center); 39 | \draw [style=simple] (7.center) to (5.center); 40 | \draw [style=simple] (5.center) to (10.center); 41 | \draw [style=simple] (10.center) to (4.center); 42 | \draw (32.center) to (31.center); 43 | \draw (31.center) to (30.center); 44 | \draw [style=simple] (34.center) to (33.center); 45 | \draw [style=simple] (33.center) to (36.center); 46 | \draw [style=simple] (36.center) to (32.center); 47 | \draw (41.center) to (40.center); 48 | \draw (40.center) to (39.center); 49 | \draw [style=simple] (43.center) to (42.center); 50 | \draw [style=simple] (42.center) to (45.center); 51 | \draw [style=simple] (45.center) to (41.center); 52 | \end{pgfonlayer} 53 | \end{tikzpicture} 54 | -------------------------------------------------------------------------------- /figures/ket-.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=none] (0) at (11.75, 0) {$\coloneqq$}; 4 | \node [style=none] (1) at (10.25, 0) {\large$\ket{-}$}; 5 | \node [style=none] (2) at (5.75, -0.5) {}; 6 | \node [style=none] (3) at (7, -0.5) {}; 7 | \node [style=none] (4) at (5.75, -2) {}; 8 | \node [style=none] (5) at (5.75, -0.5) {}; 9 | \node [style=none] (6) at (8.5, 0) {$\coloneqq$}; 10 | \node [style=none] (7) at (5.75, 1) {}; 11 | \node [style=none] (8) at (5.75, -1) {\large$-$}; 12 | \node [style=none] (9) at (13.75, 0) {$\large{\frac{1}{\sqrt{2}}}\begin{bmatrix}1\\ -1\end{bmatrix}$}; 13 | \node [style=none] (10) at (4.5, -0.5) {}; 14 | \node [style=none] (11) at (5.75, 1.75) {}; 15 | \end{pgfonlayer} 16 | \begin{pgfonlayer}{edgelayer} 17 | \draw (4.center) to (3.center); 18 | \draw (3.center) to (2.center); 19 | \draw [style=simple] (7.center) to (5.center); 20 | \draw [style=simple] (5.center) to (10.center); 21 | \draw [style=simple] (10.center) to (4.center); 22 | \end{pgfonlayer} 23 | \end{tikzpicture} 24 | -------------------------------------------------------------------------------- /figures/ket-i.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=none] (0) at (2, 0) {$\coloneqq$}; 4 | \node [style=none] (1) at (0.5, 0) {\large$\ket{-i}$}; 5 | \node [style=none] (6) at (-1.25, 0) {$\coloneqq$}; 6 | \node [style=none] (8) at (-4, -1) {\large$-i$}; 7 | \node [style=none] (9) at (4, 0) {$\large{\frac{1}{\sqrt{2}}}\begin{bmatrix}1\\ -i\end{bmatrix}$}; 8 | \node [style=none] (11) at (-4, 1.75) {}; 9 | \node [style=none] (15) at (-4, 1) {}; 10 | \node [style=none] (17) at (-2.75, -0.5) {}; 11 | \node [style=none] (18) at (-4, -2) {}; 12 | \node [style=none] (19) at (-4, -0.5) {}; 13 | \node [style=none] (20) at (-4.625, -0.5) {}; 14 | \node [style=none] (21) at (-4.625, -1.25) {}; 15 | \end{pgfonlayer} 16 | \begin{pgfonlayer}{edgelayer} 17 | \draw (18.center) to (17.center); 18 | \draw [style=simple] (19.center) to (20.center); 19 | \draw [style=simple] (20.center) to (21.center); 20 | \draw [style=simple] (21.center) to (18.center); 21 | \draw (17.center) to (19.center); 22 | \draw (18.center) to (17.center); 23 | \draw (17.center) to (19.center); 24 | \draw [style=simple] (15.center) to (19.center); 25 | \draw (18.center) to (17.center); 26 | \draw [style=simple] (15.center) to (19.center); 27 | \draw (17.center) to (19.center); 28 | \end{pgfonlayer} 29 | \end{tikzpicture} 30 | -------------------------------------------------------------------------------- /figures/ket-iconj.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=none] (0) at (12.25, 0) {$\coloneqq$}; 4 | \node [style=none] (1) at (10.25, 0) {\large$\left(\ket{-i}\right)^*$}; 5 | \node [style=none] (2) at (8.5, 0) {$\coloneqq$}; 6 | \node [style=none] (3) at (16.5, 0) {$\left(\large{\frac{1}{\sqrt{2}}}\begin{bmatrix}1\\ -i\end{bmatrix}\right)^* = \large{\frac{1}{\sqrt{2}}}\begin{bmatrix}1\\ i\end{bmatrix}$}; 7 | \node [style=none] (4) at (4.5, -0.5) {}; 8 | \node [style=none] (5) at (5.75, -2) {}; 9 | \node [style=none] (6) at (5.75, -0.5) {}; 10 | \node [style=none] (7) at (5.75, 1) {}; 11 | \node [style=none] (8) at (5.75, -1) {\large$-i$}; 12 | \node [style=none] (9) at (5.75, 1.75) {}; 13 | \node [style=none] (10) at (4.5, -0.5) {}; 14 | \node [style=none] (11) at (5.75, -2) {}; 15 | \node [style=none] (12) at (5.75, -0.5) {}; 16 | \node [style=none] (13) at (6.375, -0.5) {}; 17 | \node [style=none] (14) at (6.375, -1.25) {}; 18 | \end{pgfonlayer} 19 | \begin{pgfonlayer}{edgelayer} 20 | \draw (5.center) to (4.center); 21 | \draw [style=simple] (7.center) to (6.center); 22 | \draw (11.center) to (10.center); 23 | \draw [style=simple] (12.center) to (13.center); 24 | \draw [style=simple] (13.center) to (14.center); 25 | \draw [style=simple] (14.center) to (11.center); 26 | \draw (4.center) to (6.center); 27 | \draw (10.center) to (12.center); 28 | \end{pgfonlayer} 29 | \end{tikzpicture} 30 | -------------------------------------------------------------------------------- /figures/ket-itranspose.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=none] (0) at (12.25, 0) {$\coloneqq$}; 4 | \node [style=none] (1) at (10.25, 0) {\large$\left(\ket{-i}\right)^{\transpose}$}; 5 | \node [style=none] (2) at (8.5, 0) {$\coloneqq$}; 6 | \node [style=none] (3) at (17.5, 0) {$\left(\large{\frac{1}{\sqrt{2}}}\begin{bmatrix}1\\ -i\end{bmatrix}\right)^{\transpose} = \large{\frac{1}{\sqrt{2}}}\begin{bmatrix}1 & -i\end{bmatrix}$}; 7 | \node [style=none] (4) at (4.5, 0.25) {}; 8 | \node [style=none] (5) at (5.75, 1.75) {}; 9 | \node [style=none] (6) at (5.75, 0.25) {}; 10 | \node [style=none] (7) at (5.75, -1.25) {}; 11 | \node [style=none] (8) at (5.75, 0.75) {\large$-i$}; 12 | \node [style=none] (9) at (5.75, -2) {}; 13 | \node [style=none] (10) at (4.5, 0.25) {}; 14 | \node [style=none] (11) at (5.75, 1.75) {}; 15 | \node [style=none] (12) at (5.75, 0.25) {}; 16 | \node [style=none] (13) at (6.375, 0.25) {}; 17 | \node [style=none] (14) at (6.375, 1) {}; 18 | \end{pgfonlayer} 19 | \begin{pgfonlayer}{edgelayer} 20 | \draw (5.center) to (4.center); 21 | \draw [style=simple] (7.center) to (6.center); 22 | \draw (11.center) to (10.center); 23 | \draw [style=simple] (12.center) to (13.center); 24 | \draw [style=simple] (13.center) to (14.center); 25 | \draw [style=simple] (14.center) to (11.center); 26 | \draw (4.center) to (6.center); 27 | \draw (10.center) to (12.center); 28 | \end{pgfonlayer} 29 | \end{tikzpicture} 30 | -------------------------------------------------------------------------------- /figures/ket.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=none] (74) at (11.75, 0) {$\coloneqq$}; 4 | \node [style=none] (86) at (10.25, 0) {\large$\ket{v}$}; 5 | \node [style=none] (128) at (5.25, -0.5) {}; 6 | \node [style=none] (129) at (7, -0.5) {}; 7 | \node [style=none] (131) at (5.25, -2.5) {}; 8 | \node [style=none] (136) at (5.25, -0.5) {}; 9 | \node [style=none] (159) at (8.5, 0) {$\coloneqq$}; 10 | \node [style=none] (160) at (5.25, 2) {}; 11 | \node [style=none] (161) at (5.25, -1.25) {\large$v$}; 12 | \node [style=none] (162) at (13.75, 0) {$\begin{bmatrix}v_{1}\\ 13 | v_{2}\\ 14 | \vdots\\ v_{2^n}\end{bmatrix}$}; 15 | \node [style=none] (163) at (4, -0.5) {}; 16 | \node [style=none] (164) at (4, -1.5) {}; 17 | \end{pgfonlayer} 18 | \begin{pgfonlayer}{edgelayer} 19 | \draw (131.center) to (129.center); 20 | \draw (129.center) to (128.center); 21 | \draw [style=simple] (160.center) to (136.center); 22 | \draw [style=simple] (136.center) to (163.center); 23 | \draw [style=simple] (163.center) to (164.center); 24 | \draw [style=simple] (164.center) to (131.center); 25 | \end{pgfonlayer} 26 | \end{tikzpicture} 27 | -------------------------------------------------------------------------------- /figures/ket0.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=none] (0) at (11.75, 0) {$\coloneqq$}; 4 | \node [style=none] (1) at (10.25, 0) {\large$\kz0$}; 5 | \node [style=none] (2) at (5.75, -0.5) {}; 6 | \node [style=none] (3) at (7, -0.5) {}; 7 | \node [style=none] (4) at (5.75, -2) {}; 8 | \node [style=none] (5) at (5.75, -0.5) {}; 9 | \node [style=none] (6) at (8.5, 0) {$\coloneqq$}; 10 | \node [style=none] (7) at (5.75, 1) {}; 11 | \node [style=none] (8) at (5.75, -1) {\large$0$}; 12 | \node [style=none] (9) at (13.75, 0) {$\begin{bmatrix}1\\ 0\end{bmatrix}$}; 13 | \node [style=none] (10) at (4.5, -0.5) {}; 14 | \node [style=none] (11) at (5.75, 1.75) {}; 15 | \end{pgfonlayer} 16 | \begin{pgfonlayer}{edgelayer} 17 | \draw (4.center) to (3.center); 18 | \draw (3.center) to (2.center); 19 | \draw [style=simple] (7.center) to (5.center); 20 | \draw [style=simple] (5.center) to (10.center); 21 | \draw [style=simple] (10.center) to (4.center); 22 | \end{pgfonlayer} 23 | \end{tikzpicture} 24 | -------------------------------------------------------------------------------- /figures/ket0switch.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=none] (6) at (8.5, 0) {$=$}; 4 | \node [style=none] (19) at (11.25, 2.75) {}; 5 | \node [style=none] (26) at (5.75, 2.75) {}; 6 | \node [style=none] (38) at (7, -0.5) {}; 7 | \node [style=none] (39) at (5.75, -2) {}; 8 | \node [style=none] (40) at (5.75, -0.5) {}; 9 | \node [style=none] (41) at (5.75, -1) {\large$0$}; 10 | \node [style=none] (42) at (4.5, -0.5) {}; 11 | \node [style=none] (43) at (5.75, 2.25) {}; 12 | \node [style=none] (44) at (4.75, 0.25) {}; 13 | \node [style=none] (45) at (6.75, 0.25) {}; 14 | \node [style=none] (46) at (6.75, 1.5) {}; 15 | \node [style=none] (47) at (4.75, 1.5) {}; 16 | \node [style=none] (48) at (5.75, 1.5) {}; 17 | \node [style=none] (49) at (5.75, 0.25) {}; 18 | \node [style=none] (50) at (5.75, 1) {$\gate{NOT}$}; 19 | \node [style=none] (51) at (12.5, -0.5) {}; 20 | \node [style=none] (52) at (11.25, -2) {}; 21 | \node [style=none] (53) at (11.25, -1) {\large$1$}; 22 | \node [style=none] (54) at (10, -0.5) {}; 23 | \node 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[style=simple] (55.center) to (54.center); 44 | \end{pgfonlayer} 45 | \end{tikzpicture} 46 | -------------------------------------------------------------------------------- /figures/ket1.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=none] (0) at (11.75, 0) {$\coloneqq$}; 4 | \node [style=none] (1) at (10.25, 0) {\large$\kz1$}; 5 | \node [style=none] (2) at (5.75, -0.5) {}; 6 | \node [style=none] (3) at (7, -0.5) {}; 7 | \node [style=none] (4) at (5.75, -2) {}; 8 | \node [style=none] (5) at (5.75, -0.5) {}; 9 | \node [style=none] (6) at (8.5, 0) {$\coloneqq$}; 10 | \node [style=none] (7) at (5.75, 1) {}; 11 | \node [style=none] (8) at (5.75, -1) {\large$1$}; 12 | \node [style=none] (9) at (13.75, 0) {$\begin{bmatrix}0\\ 1\end{bmatrix}$}; 13 | \node [style=none] (10) at (4.5, -0.5) {}; 14 | \node [style=none] (11) at (5.75, 1.75) {}; 15 | \end{pgfonlayer} 16 | \begin{pgfonlayer}{edgelayer} 17 | \draw (4.center) to (3.center); 18 | \draw (3.center) to (2.center); 19 | \draw [style=simple] (7.center) to (5.center); 20 | \draw [style=simple] (5.center) to (10.center); 21 | \draw [style=simple] (10.center) to (4.center); 22 | \end{pgfonlayer} 23 | \end{tikzpicture} 24 | -------------------------------------------------------------------------------- /figures/ket1switch.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=none] (3) at (7, -0.5) {}; 4 | \node [style=none] (4) at (5.75, -2) {}; 5 | \node [style=none] (6) at (8.5, 0) {$=$}; 6 | \node [style=none] (8) at (5.75, -1) {\large$0$}; 7 | \node [style=none] (10) at (4.5, -0.5) {}; 8 | \node [style=none] (13) at (12.5, -0.5) {}; 9 | \node [style=none] (14) at (11.25, -2) {}; 10 | \node [style=none] (15) at (11.25, -0.5) {}; 11 | \node [style=none] (17) at (11.25, -1) {\large$1$}; 12 | \node [style=none] (18) at (10, -0.5) {}; 13 | \node [style=none] (19) at (11.25, 2.75) {}; 14 | \node [style=none] (26) at (5.75, 2.75) {}; 15 | \node [style=none] (28) at (11.25, 2.25) {}; 16 | \node [style=none] (29) at (10.25, 0.25) {}; 17 | \node [style=none] (30) at (12.25, 0.25) {}; 18 | \node [style=none] (31) at (12.25, 1.5) {}; 19 | \node [style=none] (32) at (10.25, 1.5) {}; 20 | \node [style=none] (33) at (11.25, 1.5) {}; 21 | \node [style=none] (34) at (11.25, 0.25) {}; 22 | \node [style=none] (35) at (11.25, 1) {$\gate{NOT}$}; 23 | \node [style=none] (36) at (5.75, -0.5) {}; 24 | \node [style=none] (37) at (5.75, 2.25) {}; 25 | \end{pgfonlayer} 26 | \begin{pgfonlayer}{edgelayer} 27 | \draw (4.center) to (3.center); 28 | \draw [style=simple] (10.center) to (4.center); 29 | \draw (14.center) to (13.center); 30 | \draw [style=simple] (15.center) to (18.center); 31 | \draw [style=simple] (18.center) to (14.center); 32 | \draw [style=simple] (29.center) to (34.center); 33 | \draw [style=simple] (34.center) to (30.center); 34 | \draw [style=simple] (30.center) to (31.center); 35 | \draw [style=simple] (31.center) to (33.center); 36 | \draw [style=simple] (33.center) to (32.center); 37 | \draw [style=simple] (32.center) to (29.center); 38 | \draw [style=simple] (28.center) to (33.center); 39 | \draw [style=simple, in=90, out=-90] (37.center) to (36.center); 40 | \draw [style=simple, in=90, out=-90] (34.center) to (15.center); 41 | \draw (3.center) to (36.center); 42 | \draw [style=simple] (36.center) to (10.center); 43 | \draw (13.center) to (15.center); 44 | \end{pgfonlayer} 45 | \end{tikzpicture} 46 | -------------------------------------------------------------------------------- /figures/ket_doubled.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=none] (6) at (0, 0) {$\leftrightsquigarrow$}; 4 | \node [style=none] (8) at (-2.25, 0) {\large$\psi$}; 5 | \node [style=none] (27) at (-1, 0.5) {}; 6 | \node [style=none] (28) at (-2.25, -1) {}; 7 | \node [style=none] (29) at (-2.25, 0.5) {}; 8 | \node [style=none] (30) at (-2.25, 2) {}; 9 | \node [style=none] (33) at (-1, 0.5) {}; 10 | \node [style=none] (34) at (-2.25, -1) {}; 11 | \node [style=none] (35) at (-2.25, 0.5) {}; 12 | \node [style=none] (36) at (-2.875, 0.5) {}; 13 | \node [style=none] (37) at (-2.875, -0.25) {}; 14 | \node [style=none] (38) at (1.875, 1.25) {\large$\psi$}; 15 | \node [style=none] (39) at (3.125, 1.75) {}; 16 | \node [style=none] (40) at (1.875, 0.25) {}; 17 | \node [style=none] (41) at (1.875, 1.75) {}; 18 | \node [style=none] (42) at (1.875, 2.75) {}; 19 | \node [style=none] (43) at (1.875, 3.5) {}; 20 | \node [style=none] (44) at (3.125, 1.75) {}; 21 | \node [style=none] (45) at (1.875, 0.25) {}; 22 | \node [style=none] (46) at (1.875, 1.75) {}; 23 | \node [style=none] (47) at (1.25, 1.75) {}; 24 | \node [style=none] (48) at (1.25, 1) {}; 25 | \node [style=none] (49) at (1.875, -1.25) {\large$\psi$}; 26 | \node [style=none] (50) at (3.125, -1.75) {}; 27 | \node [style=none] (51) at (1.875, -0.25) {}; 28 | \node [style=none] (52) at (1.875, -1.75) {}; 29 | \node [style=none] (53) at (1.875, -2.75) {}; 30 | \node [style=none] (54) at (1.875, -3.5) {}; 31 | \node [style=none] (55) at (3.125, -1.75) {}; 32 | \node [style=none] (56) at (1.875, -0.25) {}; 33 | \node [style=none] (57) at (1.875, -1.75) {}; 34 | \node [style=none] (58) at (1.25, -1.75) {}; 35 | \node [style=none] (59) at (1.25, -1) {}; 36 | \end{pgfonlayer} 37 | \begin{pgfonlayer}{edgelayer} 38 | \draw (28.center) to (27.center); 39 | \draw [style=simple] (30.center) to (29.center); 40 | \draw (34.center) to (33.center); 41 | \draw [style=simple] (35.center) to (36.center); 42 | \draw [style=simple] (36.center) to (37.center); 43 | \draw [style=simple] (37.center) to (34.center); 44 | \draw (27.center) to (29.center); 45 | \draw (33.center) to (35.center); 46 | \draw (40.center) to (39.center); 47 | \draw [style=simple] (42.center) to (41.center); 48 | \draw (45.center) to (44.center); 49 | \draw [style=simple] (46.center) to (47.center); 50 | \draw [style=simple] (47.center) to (48.center); 51 | \draw [style=simple] (48.center) to (45.center); 52 | \draw (39.center) to (41.center); 53 | \draw (44.center) to (46.center); 54 | \draw (51.center) to (50.center); 55 | \draw [style=simple] (53.center) to (52.center); 56 | \draw (56.center) to (55.center); 57 | \draw [style=simple] (57.center) to (58.center); 58 | \draw [style=simple] (58.center) to (59.center); 59 | \draw [style=simple] (59.center) to (56.center); 60 | \draw (50.center) to (52.center); 61 | \draw (55.center) to (57.center); 62 | \end{pgfonlayer} 63 | \end{tikzpicture} 64 | -------------------------------------------------------------------------------- /figures/ketpsi.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=none] (2) at (5.75, -0.5) {}; 4 | \node [style=none] (3) at (7, -0.5) {}; 5 | \node [style=none] (4) at (5.75, -2) {}; 6 | \node [style=none] (5) at (5.75, -0.5) {}; 7 | \node [style=none] (6) at (8, 0) {$=$}; 8 | \node [style=none] (7) at (5.75, 1) {}; 9 | \node [style=none] (8) at (5.75, -1) {\large$\psi$}; 10 | \node [style=none] (11) at (5.75, 1.75) {}; 11 | \node [style=none] (12) at (15, 0) {$\kx{\psi} = \begin{bmatrix}\alpha\\ \beta\end{bmatrix} = \alpha\begin{bmatrix}1\\ 0\end{bmatrix} + \beta\begin{bmatrix}0\\ 1\end{bmatrix} = \alpha\kz0 + \beta\kz1$}; 12 | \node [style=none] (13) at (5.125, -0.5) {}; 13 | \node [style=none] (14) at (5.125, -1.25) {}; 14 | \end{pgfonlayer} 15 | \begin{pgfonlayer}{edgelayer} 16 | \draw (4.center) to (3.center); 17 | \draw (3.center) to (2.center); 18 | \draw [style=simple] (7.center) to (5.center); 19 | \draw [style=simple] (5.center) to (13.center); 20 | \draw [style=simple] (13.center) to (14.center); 21 | \draw [style=simple] (14.center) to (4.center); 22 | \end{pgfonlayer} 23 | \end{tikzpicture} 24 | -------------------------------------------------------------------------------- /figures/ketv.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=none] (2) at (5.75, -0.5) {}; 4 | \node [style=none] (3) at (7, -0.5) {}; 5 | \node [style=none] (4) at (5.75, -2) {}; 6 | \node [style=none] (5) at (5.75, -0.5) {}; 7 | \node [style=none] (6) at (8, 0) {$=$}; 8 | \node [style=none] (7) at (5.75, 1) {}; 9 | \node [style=none] (8) at (5.75, -1) {\large$v$}; 10 | \node [style=none] (10) at (4.5, -0.5) {}; 11 | \node [style=none] (11) at (5.75, 1.75) {}; 12 | \node [style=none] (12) at (15, 0) {$\kx{v} = \begin{bmatrix}a\\ b\end{bmatrix} = a\begin{bmatrix}1\\ 0\end{bmatrix} + b\begin{bmatrix}0\\ 1\end{bmatrix} = a\kz0 + b\kz1$}; 13 | \end{pgfonlayer} 14 | \begin{pgfonlayer}{edgelayer} 15 | \draw (4.center) to (3.center); 16 | \draw (3.center) to (2.center); 17 | \draw [style=simple] (7.center) to (5.center); 18 | \draw [style=simple] (5.center) to (10.center); 19 | \draw [style=simple] (10.center) to (4.center); 20 | \end{pgfonlayer} 21 | \end{tikzpicture} 22 | -------------------------------------------------------------------------------- /figures/nand.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=none] (0) at (3, 1.25) {}; 4 | \node [style=none] (1) at (3, -1.25) {}; 5 | \node [style=none] (2) at (5.75, 0) {}; 6 | \node [style=none] (3) at (3, 0.75) {}; 7 | \node [style=none] (4) at (3, -0.75) {}; 8 | \node [style=none] (5) at (1.25, 0.75) {}; 9 | \node [style=none] (6) at (1.25, -0.75) {}; 10 | \node [style=none] (8) at (4.25, 0) {AND}; 11 | \node [style=none] (9) at (7.5, 1.5) {}; 12 | \node 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\begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=none] (129) at (-1.5, 0.5) {}; 4 | \node [style=none] (131) at (-3.25, -1.5) {}; 5 | \node [style=none] (161) at (-3.25, -0.25) {$\psi$}; 6 | \node [style=none] (163) at (-4.5, 0.5) {}; 7 | \node [style=none] (164) at (-4.5, -0.5) {}; 8 | \node [style=none] (165) at (-3.75, 0.5) {}; 9 | \node [style=none] (166) at (-2.75, 0.5) {}; 10 | \node [style=none] (167) at (-3.75, 2.75) {}; 11 | \node [style=none] (168) at (-2.75, 2.75) {}; 12 | \node [style=none] (169) at (5.25, 0.5) {}; 13 | \node [style=none] (170) at (3.5, -1.5) {}; 14 | \node [style=none] (171) at (3.5, -0.25) {$\psi$}; 15 | \node [style=none] (172) at (2.25, 0.5) {}; 16 | \node [style=none] (173) at (2.25, -0.5) {}; 17 | \node [style=none] (174) at (3, 0.5) {}; 18 | \node [style=none] (175) at (4, 0.5) {}; 19 | \node [style=none] (176) at (1.5, 0.5) {}; 20 | \node [style=none] (177) at (4, 2.75) {}; 21 | \node [style=none] (178) at (1.5, -2.25) {}; 22 | 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directed arrow] (2.center) to (3.center); 21 | \draw [style=light right directed arrow] (5.center) to (3.center); 22 | \draw [style=light right directed arrow] (4.center) to (3.center); 23 | \draw [style=diredge0.3] (3.center) to (6.center); 24 | \draw [style=diredge0.3] (3.center) to (7.center); 25 | \draw [style=diredge0.3] (3.center) to (11.center); 26 | \draw [style=diredge0.3] (3.center) to (13.center); 27 | \end{pgfonlayer} 28 | \end{tikzpicture} 29 | -------------------------------------------------------------------------------- /figures/unitcircle01.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=unit circle] (0) at (0, 0) {}; 4 | \node [style=none] (1) at (0, 4.25) {}; 5 | \node [style=none] (2) at (4.25, 0) {}; 6 | \node [style=none] (3) at (0, 0) {}; 7 | \node [style=none] (4) at (-4.25, 0) {}; 8 | \node [style=none] (5) at (0, -4.25) {}; 9 | \node [style=none] (6) at (0, 4.25) {}; 10 | \node [style=none] (8) at (0, 4.75) {$\ket{\,1\,}$}; 11 | \node [style=none] (9) at (5, 0) {$\ket{\,0\,}$}; 12 | \node [style=none] (13) at (4.25, 0) {}; 13 | \end{pgfonlayer} 14 | \begin{pgfonlayer}{edgelayer} 15 | \draw [style=light right directed arrow] (1.center) to (3.center); 16 | \draw [style=light right directed arrow] (2.center) to (3.center); 17 | \draw [style=light right directed arrow, in=270, out=90] (5.center) to (3.center); 18 | \draw [style=light right directed arrow] (4.center) to (3.center); 19 | \draw [style=diredge0.3] (3.center) to (6.center); 20 | \draw [style=diredge0.3] (3.center) to (13.center); 21 | \end{pgfonlayer} 22 | \end{tikzpicture} 23 | -------------------------------------------------------------------------------- /figures/unitcirclehopposite.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=unit circle] (0) at (4.75, 1) {}; 4 | \node [style=none] (3) at (4.75, 1) {}; 5 | \node [style=none] (1) at (4.75, 5.25) {}; 6 | \node [style=none] (2) at (9, 1) {}; 7 | \node [style=none] (4) at (0.5, 1) {}; 8 | \node [style=none] (5) at (4.75, -3.25) {}; 9 | \node [style=none] (6) at (7.75, 4) {}; 10 | \node [style=none] (7) at (9.75, 1) {$\ket{\,0\,}$}; 11 | \node [style=none] (8) at (8.25, 4.5) {$\ket{+}$}; 12 | \node [style=none] (9) at (9, 1) {}; 13 | \node [style=none] (26) at (4.75, 1) {}; 14 | \node [style=none] (27) at (4.75, 5.25) {}; 15 | \node [style=none] (28) at (4.75, 5.75) {$\ket{\,1\,}$}; 16 | \node [style=none] (29) at (7.75, -2) {}; 17 | \node [style=none] (30) at (8.25, -2.5) {$\ket{-}$}; 18 | \node [style=none] (33) at (7.825, -1.925) {}; 19 | \node [style=none] (34) at (4.85, 5.25) {}; 20 | \node [style=none] (43) at (8.975, 1.125) {}; 21 | \node [style=none] (44) at (7.825, 3.9) {}; 22 | \node [style=none] (72) at (1.65, 3.925) {}; 23 | \node [style=none] (73) at (4.625, -3.25) {}; 24 | \node [style=none] (74) at (0.5, 0.875) {}; 25 | \node [style=none] (75) at (1.65, -1.9) {}; 26 | \node [style=none] (76) at (3.1, 4.925) {}; 27 | \node [style=none] (77) at (6.375, -2.925) {}; 28 | \end{pgfonlayer} 29 | \begin{pgfonlayer}{edgelayer} 30 | \draw [style=light right directed arrow] (1.center) to (3.center); 31 | \draw [style=light right directed arrow] (2.center) to (3.center); 32 | \draw [style=light right directed arrow] (5.center) to (3.center); 33 | \draw [style=light right directed arrow] (4.center) to (3.center); 34 | \draw [style=diredge0.3] (3.center) to (6.center); 35 | \draw [style=diredge0.3] (3.center) to (9.center); 36 | \draw [style=diredge0.3] (26.center) to (27.center); 37 | \draw [style=diredge0.3] (26.center) to (29.center); 38 | \draw [style=hadamard arrows] (34.center) to (33.center); 39 | \draw [style=hadamard arrows] (44.center) to (43.center); 40 | \draw [style=hadamard arrows] (73.center) to (72.center); 41 | \draw [style=hadamard arrows] (75.center) to (74.center); 42 | \draw [style=hadamard arrows] (77.center) to (76.center); 43 | \end{pgfonlayer} 44 | \end{tikzpicture} 45 | -------------------------------------------------------------------------------- /figures/unitcirclehreflect.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=unit circle] (0) at (-2.25, 1) {}; 4 | \node [style=none] (1) at (-2.25, 5.25) {}; 5 | \node [style=none] (2) at (2, 1) {}; 6 | \node [style=none] (3) at (-2.25, 1) {}; 7 | \node [style=none] (4) at (-6.5, 1) {}; 8 | \node [style=none] (5) at (-2.25, -3.25) {}; 9 | \node [style=none] (7) at (0.75, 4) {}; 10 | \node [style=none] (9) at (2.75, 1) {$\ket{\,0\,}$}; 11 | \node [style=none] (10) at (1.25, 4.5) {$\ket{+}$}; 12 | \node [style=none] (13) at (2, 1) {}; 13 | \node [style=unit circle] (14) at (13.75, 1) {}; 14 | \node [style=none] (15) at (13.75, 5.25) {}; 15 | \node [style=none] (16) at (18, 1) {}; 16 | \node [style=none] (17) at (13.75, 1) {}; 17 | \node [style=none] (18) at (9.5, 1) {}; 18 | \node [style=none] (19) at (13.75, -3.25) {}; 19 | \node [style=none] (20) at (13.75, 5.25) {}; 20 | \node [style=none] (22) at (13.75, 5.75) {$\ket{\,1\,}$}; 21 | \node [style=none] (25) at (16.75, -2) {}; 22 | \node [style=none] (26) at (17.25, -2.5) {$\ket{-}$}; 23 | \node [style=none] (28) at (1.75, 2.5) {}; 24 | \node [style=none] (29) at (-6.25, -0.5) {}; 25 | \node [style=none] (30) at (17.75, 2.5) {}; 26 | \node [style=none] (31) at (9.75, -0.5) {}; 27 | \end{pgfonlayer} 28 | \begin{pgfonlayer}{edgelayer} 29 | \draw [style=light right directed arrow] (1.center) to (3.center); 30 | \draw [style=light right directed arrow] (2.center) to (3.center); 31 | \draw [style=light right directed arrow] (5.center) to (3.center); 32 | \draw [style=light right directed arrow] (4.center) to (3.center); 33 | \draw [style=diredge0.3] (3.center) to (7.center); 34 | \draw [style=diredge0.3] (3.center) to (13.center); 35 | \draw [style=light right directed arrow] (15.center) to (17.center); 36 | \draw [style=light right directed arrow] (16.center) to (17.center); 37 | \draw [style=light right directed arrow] (19.center) to (17.center); 38 | \draw [style=light right directed arrow] (18.center) to (17.center); 39 | \draw [style=diredge0.3] (17.center) to (20.center); 40 | \draw [style=diredge0.3] (17.center) to (25.center); 41 | \draw [style=dashed edge] (29.center) to (28.center); 42 | \draw [style=dashed edge] (31.center) to (30.center); 43 | \end{pgfonlayer} 44 | \end{tikzpicture} 45 | -------------------------------------------------------------------------------- /figures/unitcirclex.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=unit circle] (0) at (4.75, 1) {}; 4 | \node [style=none] (1) at (4.75, 5.25) {}; 5 | \node [style=none] (2) at (9, 1) {}; 6 | \node [style=none] (3) at (4.75, 1) {}; 7 | \node [style=none] (4) at (0.5, 1) {}; 8 | \node [style=none] (5) at (4.75, -3.25) {}; 9 | \node [style=none] (6) at (7.75, 4) {}; 10 | \node [style=none] (7) at (8.25, 4.5) {$\ket{+}$}; 11 | \node [style=none] (8) at (1.75, -2) {}; 12 | \end{pgfonlayer} 13 | \begin{pgfonlayer}{edgelayer} 14 | \draw [style=light right directed arrow] (1.center) to (3.center); 15 | \draw [style=light right directed arrow] (2.center) to (3.center); 16 | \draw [style=light right directed arrow] (5.center) to (3.center); 17 | \draw [style=light right directed arrow] (4.center) to (3.center); 18 | \draw [style=diredge0.3] (3.center) to (6.center); 19 | \draw [style=dashed edge] (6.center) to (8.center); 20 | \end{pgfonlayer} 21 | \end{tikzpicture} 22 | -------------------------------------------------------------------------------- /figures/unitcirclexex.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=unit circle] (14) at (13.75, 1) {}; 4 | \node [style=none] (15) at (13.75, 5.25) {}; 5 | \node [style=none] (16) at (18, 1) {}; 6 | \node [style=none] (17) at (13.75, 1) {}; 7 | \node [style=none] (18) at (9.5, 1) {}; 8 | \node [style=none] (19) at (13.75, -3.25) {}; 9 | \node [style=none] (20) at (13.75, 5.25) {}; 10 | \node [style=none] (22) at (13.75, 5.75) {$\ket{\,1\,}$}; 11 | \node [style=none] (23) at (18.75, 1) {$\ket{\,0\,}$}; 12 | \node [style=none] (27) at (18, 1) {}; 13 | \node [style=none] (53) at (16.75, 4) {}; 14 | \node [style=none] (54) at (10.75, -2) {}; 15 | \node [style=unit circle] (79) at (29.75, 1) {}; 16 | \node [style=none] (80) at (29.75, 5.25) {}; 17 | \node [style=none] (81) at (34, 1) {}; 18 | \node [style=none] (82) at (29.75, 1) {}; 19 | \node [style=none] (83) at (25.5, 1) {}; 20 | \node [style=none] (84) at (29.75, -3.25) {}; 21 | \node [style=none] (90) at (32.75, -2) {}; 22 | \node [style=none] (91) at (33.25, -2.5) {$\ket{-}$}; 23 | \node [style=none] (94) at (29.75, 1) {}; 24 | \node [style=none] (95) at (26.75, 4) {}; 25 | \node [style=none] (96) at (26.25, 4.5) {$\texttt{-}\ket{-}$}; 26 | \node [style=none] (97) at (32.75, 4) {}; 27 | \node [style=none] (98) at (26.75, -2) {}; 28 | \end{pgfonlayer} 29 | \begin{pgfonlayer}{edgelayer} 30 | \draw [style=light right directed arrow] (15.center) to (17.center); 31 | \draw [style=light right directed arrow] (16.center) to (17.center); 32 | \draw [style=light right directed arrow] (19.center) to (17.center); 33 | \draw [style=light right directed arrow] (18.center) to (17.center); 34 | \draw [style=diredge0.3] (17.center) to (20.center); 35 | \draw [style=diredge0.3] (17.center) to (27.center); 36 | \draw [style=dashed edge] (53.center) to (54.center); 37 | \draw [style=light right directed arrow] (80.center) to (82.center); 38 | \draw [style=light right directed arrow] (81.center) to (82.center); 39 | \draw [style=light right directed arrow] (84.center) to (82.center); 40 | \draw [style=light right directed arrow] (83.center) to (82.center); 41 | \draw [style=diredge0.3] (82.center) to (90.center); 42 | \draw [style=diredge0.3] (94.center) to (95.center); 43 | \draw [style=dashed edge] (97.center) to (98.center); 44 | \end{pgfonlayer} 45 | \end{tikzpicture} 46 | -------------------------------------------------------------------------------- /figures/unitcirclez.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=unit circle] (0) at (4.75, 1) {}; 4 | \node [style=none] (1) at (4.75, 5.25) {}; 5 | \node [style=none] (2) at (9, 1) {}; 6 | \node [style=none] (3) at (4.75, 1) {}; 7 | \node [style=none] (4) at (0.5, 1) {}; 8 | \node [style=none] (5) at (4.75, -3.25) {}; 9 | \node [style=none] (6) at (9, 1) {}; 10 | \node [style=none] (16) at (9.75, 1) {$\ket{\,0\,}$}; 11 | \node [style=none] (18) at (0.5, 1) {}; 12 | \end{pgfonlayer} 13 | \begin{pgfonlayer}{edgelayer} 14 | \draw [style=light right directed arrow] (1.center) to (3.center); 15 | \draw [style=light right directed arrow] (2.center) to (3.center); 16 | \draw [style=light right directed arrow] (5.center) to (3.center); 17 | \draw [style=light right directed arrow] (4.center) to (3.center); 18 | \draw [style=diredge0.3] (3.center) to (6.center); 19 | \draw [style=dashed edge] (6.center) to (18.center); 20 | \end{pgfonlayer} 21 | \end{tikzpicture} 22 | -------------------------------------------------------------------------------- /figures/unitcirclezex.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=unit circle] (0) at (20.75, 1) {}; 4 | \node [style=none] (1) at (20.75, 5.25) {}; 5 | \node [style=none] (2) at (25, 1) {}; 6 | \node [style=none] (3) at (20.75, 1) {}; 7 | \node [style=none] (4) at (16.5, 1) {}; 8 | \node [style=none] (5) at (20.75, -3.25) {}; 9 | \node [style=none] (6) at (23.75, -2) {}; 10 | \node [style=none] (7) at (36.75, 5.75) {$\ket{\,1\,}$}; 11 | \node [style=none] (8) at (23.75, 4) {}; 12 | \node [style=unit circle] (9) at (36.75, 1) {}; 13 | \node [style=none] (10) at (36.75, 5.25) {}; 14 | \node [style=none] (11) at (41, 1) {}; 15 | \node [style=none] (12) at (36.75, 1) {}; 16 | \node [style=none] (13) at (32.5, 1) {}; 17 | \node [style=none] (14) at (36.75, -3.25) {}; 18 | \node [style=none] (15) at (36.75, -3.25) {}; 19 | \node [style=none] (16) at (36.75, 1) {}; 20 | \node [style=none] (17) at (36.75, 5.25) {}; 21 | \node [style=none] (18) at (36.75, -3.75) {$\texttt{-}\ket{\,1\,}$}; 22 | \node [style=none] (19) at (41, 1) {}; 23 | \node [style=none] (20) at (32.5, 1) {}; 24 | \node [style=none] (21) at (24.25, 4.5) {$\ket{+}$}; 25 | \node [style=none] (22) at (25, 1) {}; 26 | \node [style=none] (23) at (24.25, -2.5) {$\ket{-}$}; 27 | \node [style=none] (24) at (25, 1) {}; 28 | \node [style=none] (25) at (16.5, 1) {}; 29 | \end{pgfonlayer} 30 | \begin{pgfonlayer}{edgelayer} 31 | \draw [style=light right directed arrow] (1.center) to (3.center); 32 | \draw [style=light right directed arrow] (2.center) to (3.center); 33 | \draw [style=light right directed arrow] (5.center) to (3.center); 34 | \draw [style=light right directed arrow] (4.center) to (3.center); 35 | \draw [style=diredge0.3] (3.center) to (6.center); 36 | \draw [style=diredge0.3] (3.center) to (8.center); 37 | \draw [style=light right directed arrow] (10.center) to (12.center); 38 | \draw [style=light right directed arrow] (11.center) to (12.center); 39 | \draw [style=light right directed arrow] (14.center) to (12.center); 40 | \draw [style=light right directed arrow] (13.center) to (12.center); 41 | \draw [style=diredge0.3] (12.center) to (15.center); 42 | \draw [style=diredge0.3] (16.center) to (17.center); 43 | \draw [style=dashed edge] (19.center) to (20.center); 44 | \draw [style=dashed edge] (24.center) to (25.center); 45 | \end{pgfonlayer} 46 | \end{tikzpicture} 47 | -------------------------------------------------------------------------------- /figures/x_circuitmodel.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=targ] (0) at (0, 0) {\large$+$}; 4 | \node [style=none] (1) at (1, 0) {}; 5 | \node [style=none] (2) at (-1, 0) {}; 6 | \end{pgfonlayer} 7 | \begin{pgfonlayer}{edgelayer} 8 | \draw [style=simple] (2.center) to (0); 9 | \draw [style=simple] (0) to (1.center); 10 | \end{pgfonlayer} 11 | \end{tikzpicture} 12 | -------------------------------------------------------------------------------- /figures/x_circuitmodel2.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=box] (0) at (0, 0) {$X$}; 4 | \node [style=none] (1) at (1, 0) {}; 5 | \node [style=none] (2) at (-1, 0) {}; 6 | \end{pgfonlayer} 7 | \begin{pgfonlayer}{edgelayer} 8 | \draw [style=simple] (2.center) to (0); 9 | \draw [style=simple] (0) to (1.center); 10 | \end{pgfonlayer} 11 | \end{tikzpicture} 12 | -------------------------------------------------------------------------------- /figures/yank.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=none] (0) at (-3.25, 0.5) {}; 4 | \node [style=none] (1) at (-1.75, -0.5) {}; 5 | \node [style=none] (2) at (-1, 1) {}; 6 | \node [style=none] (4) at (-4, -1) {}; 7 | \node [style=none] (5) at (0, 0) {$=$}; 8 | \node [style=none] (6) at (1, 0) {}; 9 | \node [style=none] (7) at (4, 0) {}; 10 | \end{pgfonlayer} 11 | \begin{pgfonlayer}{edgelayer} 12 | \draw [in=90, out=-90] (0.center) to (1.center); 13 | \draw [style=simple, in=-180, out=90, looseness=0.75] (0.center) to (2.center); 14 | \draw [style=simple, in=-90, out=0, looseness=0.50] (4.center) to (1.center); 15 | \draw [style=simple, in=0, out=-180] (7.center) to (6.center); 16 | \end{pgfonlayer} 17 | \end{tikzpicture} 18 | -------------------------------------------------------------------------------- /figures/yank2.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=none] (0) at (-3.25, -0.5) {}; 4 | \node [style=none] (1) at (-1.75, 0.5) {}; 5 | \node [style=none] (2) at (-1, -1) {}; 6 | \node [style=none] (4) at (-4, 1) {}; 7 | \node [style=none] (5) at (0, 0) {$=$}; 8 | \node [style=none] (6) at (1, 0) {}; 9 | \node [style=none] (7) at (4, 0) {}; 10 | \end{pgfonlayer} 11 | \begin{pgfonlayer}{edgelayer} 12 | \draw [in=-90, out=90] (0.center) to (1.center); 13 | \draw [style=simple, in=180, out=-90, looseness=0.75] (0.center) to (2.center); 14 | \draw [style=simple, in=90, out=0, looseness=0.50] (4.center) to (1.center); 15 | \draw [style=simple, in=0, out=180] (7.center) to (6.center); 16 | \end{pgfonlayer} 17 | \end{tikzpicture} 18 | -------------------------------------------------------------------------------- /figures/yankZ.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=Z dot] (0) at (-3.25, 0.5) {}; 4 | \node [style=Z dot] (1) at (-1.75, -0.5) {}; 5 | \node [style=none] (2) at (-1, 1) {}; 6 | \node [style=none] (4) at (-4, -1) {}; 7 | \node [style=none] (5) at (0, 0) {$=$}; 8 | \node [style=Z dot] (9) at (2.5, 0) {}; 9 | \node [style=none] (10) at (4, 1) {}; 10 | \node [style=none] (11) at (1, -1) {}; 11 | \node [style=none] (15) at (-8.25, 0.5) {}; 12 | \node [style=none] (16) at (-6.75, -0.5) {}; 13 | \node [style=none] (17) at (-6, 1) {}; 14 | \node [style=none] (18) at (-9, -1) {}; 15 | \node [style=none] (19) at (-5, 0) {$=$}; 16 | \node [style=none] (20) at (5, 0) {$=$}; 17 | \node [style=Z dot] (21) at (7.5, 0) {}; 18 | \node [style=none] (22) at (9, 0) {}; 19 | \node [style=none] (23) at (6, 0) {}; 20 | \node [style=none] (24) at (10, 0) {$=$}; 21 | \node [style=none] (25) at (12.5, 0) {}; 22 | \node [style=none] (26) at (14, 0) {}; 23 | \node [style=none] (27) at (11, 0) {}; 24 | \end{pgfonlayer} 25 | \begin{pgfonlayer}{edgelayer} 26 | \draw [in=90, out=-90] (0) to (1); 27 | \draw [style=simple, in=-180, out=90, looseness=0.75] (0) to (2.center); 28 | \draw [style=simple, in=-90, out=0, looseness=0.50] (4.center) to (1); 29 | \draw [style=simple, in=-120, out=0] (11.center) to (9); 30 | \draw [style=simple, in=-180, out=60] (9) to (10.center); 31 | \draw [in=90, out=-90] (15.center) to (16.center); 32 | \draw [style=simple, in=-180, out=90, looseness=0.75] (15.center) to (17.center); 33 | \draw [style=simple, in=-90, out=0, looseness=0.50] (18.center) to (16.center); 34 | \draw [style=simple] (23.center) to (21); 35 | \draw [style=simple] (21) to (22.center); 36 | \draw [style=simple] (27.center) to (25.center); 37 | \draw [style=simple] (25.center) to (26.center); 38 | \end{pgfonlayer} 39 | \end{tikzpicture} 40 | -------------------------------------------------------------------------------- /figures/zxCX.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=none] (2) at (0, 0) {$\leftrightsquigarrow$}; 4 | \node [style=small dot] (15) at (3, 0.75) {}; 5 | \node [style=targ] (16) at (3, -0.75) {\large$+$}; 6 | \node [style=none] (17) at (4.25, 0.75) {}; 7 | \node [style=none] (18) at (4.25, -0.75) {}; 8 | \node [style=none] (19) at (1.75, 0.75) {}; 9 | \node [style=none] (20) at (1.75, -0.75) {}; 10 | \node [style=Z dot] (21) at (-3, 0.75) {}; 11 | \node [style=X dot] (22) at (-3, -0.75) {}; 12 | \node [style=none] (23) at (-1.75, 0.75) {}; 13 | \node [style=none] 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\end{tikzpicture} 36 | -------------------------------------------------------------------------------- /figures/zxH.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=none] (2) at (0, 0) {$\coloneqq$}; 4 | \node [style=none] (9) at (1.75, 0) {}; 5 | \node [style=box] (10) at (3, 0) {$H$}; 6 | \node [style=none] (11) at (4.25, 0) {}; 7 | \node [style=none] (12) at (-4.25, 0) {}; 8 | \node [style=hadamard] (13) at (-3, 0) {}; 9 | \node [style=none] (14) at (-1.75, 0) {}; 10 | \end{pgfonlayer} 11 | \begin{pgfonlayer}{edgelayer} 12 | \draw [style=simple] (10) to (11.center); 13 | \draw [style=simple] (10) to (9.center); 14 | \draw [style=simple] (13) to (14.center); 15 | \draw [style=simple] (13) to (12.center); 16 | \end{pgfonlayer} 17 | \end{tikzpicture} 18 | -------------------------------------------------------------------------------- /figures/zxHEuler1.tikz: 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\end{pgfonlayer} 22 | \end{tikzpicture} 23 | -------------------------------------------------------------------------------- /figures/zxHEuler2.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=none] (1) at (7.75, 0) {}; 4 | \node [style=X phase dot] (4) at (3, 0) {$\frac{\pi}{2}$}; 5 | \node [style=none] (5) at (1.5, 0) {}; 6 | \node [style=none] (6) at (-1.25, 0) {}; 7 | \node [style=box] (7) at (-2.5, 0) {$H$}; 8 | \node [style=none] (8) at (-3.75, 0) {}; 9 | \node [style=none] (9) at (0, 0) {$=$}; 10 | \node [style=Z phase dot] (10) at (4.75, 0) {$\frac{\pi}{2}$}; 11 | \node [style=X phase dot] (11) at (6.5, 0) {$\frac{\pi}{2}$}; 12 | \node [style=none] (12) at (1.5, 1) {$e^{-\frac{i \pi}{4}}$}; 13 | \end{pgfonlayer} 14 | \begin{pgfonlayer}{edgelayer} 15 | \draw [style=simple] (4) to (5.center); 16 | \draw [style=simple] (7) to (8.center); 17 | \draw [style=simple] (7) to (6.center); 18 | \draw [style=simple] (4) to (10); 19 | \draw [style=simple] (10) to (11); 20 | \draw [style=simple] (11) to (1.center); 21 | \end{pgfonlayer} 22 | \end{tikzpicture} 23 | -------------------------------------------------------------------------------- /figures/zxHH.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=none] (2) at (0, 0) {$=$}; 4 | \node [style=none] (9) at (1.75, 0) {}; 5 | \node [style=none] (11) at (4.25, 0) {}; 6 | \node [style=hadamard] (13) at (-3, 0) {}; 7 | \node [style=none] (14) at (-1.75, 0) {}; 8 | \node [style=hadamard] (16) at (-4.25, 0) {}; 9 | \node [style=none] (17) at (-5.5, 0) {}; 10 | \end{pgfonlayer} 11 | \begin{pgfonlayer}{edgelayer} 12 | \draw [style=simple] (13) to (14.center); 13 | \draw [style=simple] (16) to (17.center); 14 | \draw [style=simple] (13) to (16); 15 | \draw [style=simple] (11.center) to (9.center); 16 | \end{pgfonlayer} 17 | \end{tikzpicture} 18 | -------------------------------------------------------------------------------- /figures/zxHedge.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=none] (2) at (0, 0) {$\coloneqq$}; 4 | \node [style=none] (9) at (1.75, 0) {}; 5 | \node [style=box] (10) at (3, 0) {$H$}; 6 | \node [style=none] (11) at (4.25, 0) {}; 7 | \node [style=none] (12) at (-4.25, 0) {}; 8 | \node [style=none] (14) at (-1.75, 0) {}; 9 | \end{pgfonlayer} 10 | \begin{pgfonlayer}{edgelayer} 11 | \draw [style=simple] (10) to (11.center); 12 | \draw [style=simple] (10) to (9.center); 13 | \draw [style=hadamard edge] (12.center) to (14.center); 14 | \end{pgfonlayer} 15 | \end{tikzpicture} 16 | -------------------------------------------------------------------------------- /figures/zxS.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=none] (2) at (0, 0) {$\leftrightsquigarrow$}; 4 | \node [style=none] (9) at (1.75, 0) {}; 5 | \node [style=box] (10) at (3, 0) {$S$}; 6 | \node [style=none] (11) at (4.25, 0) {}; 7 | \node [style=none] (12) at (-4.25, 0) {}; 8 | \node [style=Z phase dot] (13) at (-3, 0) {$\frac{\pi}{2}$}; 9 | \node [style=none] (14) at (-1.75, 0) {}; 10 | \end{pgfonlayer} 11 | \begin{pgfonlayer}{edgelayer} 12 | \draw [style=simple] (10) to (11.center); 13 | \draw [style=simple] (10) to (9.center); 14 | \draw [style=simple] (13) to (14.center); 15 | \draw [style=simple] (13) to (12.center); 16 | \end{pgfonlayer} 17 | \end{tikzpicture} 18 | -------------------------------------------------------------------------------- /figures/zxT.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=none] (2) at (0, 0) {$\leftrightsquigarrow$}; 4 | \node [style=none] (9) at (1.75, 0) {}; 5 | \node [style=box] (10) at (3, 0) {$T$}; 6 | \node [style=none] (11) at (4.25, 0) {}; 7 | \node [style=none] (12) at (-4.25, 0) {}; 8 | \node [style=Z phase dot] (13) at (-3, 0) {$\frac{\pi}{4}$}; 9 | \node [style=none] (14) at (-1.75, 0) {}; 10 | \end{pgfonlayer} 11 | \begin{pgfonlayer}{edgelayer} 12 | \draw [style=simple] (10) to (11.center); 13 | \draw [style=simple] (10) to (9.center); 14 | \draw [style=simple] (13) to (14.center); 15 | \draw [style=simple] (13) to (12.center); 16 | \end{pgfonlayer} 17 | \end{tikzpicture} 18 | -------------------------------------------------------------------------------- /figures/zxX.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=none] (1) at (-1.75, 0) {}; 4 | \node [style=none] (2) at (0, 0) {$=$}; 5 | \node [style=X phase dot] (4) at (-3, 0) {$\pi$}; 6 | \node [style=none] (5) at (-4.25, 0) {}; 7 | \node [style=none] (6) at (4.25, 0) {}; 8 | \node [style=box] (7) at (3, 0) {$X$}; 9 | \node [style=none] (8) at (1.75, 0) {}; 10 | \end{pgfonlayer} 11 | \begin{pgfonlayer}{edgelayer} 12 | \draw [style=simple] (4) to (5.center); 13 | \draw [style=simple] (4) to (1.center); 14 | \draw [style=simple] (7) to (8.center); 15 | \draw [style=simple] (7) to (6.center); 16 | \end{pgfonlayer} 17 | \end{tikzpicture} 18 | -------------------------------------------------------------------------------- /figures/zxXI.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=none] (1) at (-1.75, 0) {}; 4 | \node [style=X dot] (4) at (-3, 0) {}; 5 | \node [style=none] (5) at (-4.25, 0) {}; 6 | \node [style=none] (6) at (0, 0) {$=$}; 7 | \node [style=none] (7) at (4.25, 0) {}; 8 | \node [style=X phase dot] (8) at (3, 0) {$0$}; 9 | \node [style=none] (9) at (1.75, 0) {}; 10 | \node [style=none] (10) at (7.75, 0) {}; 11 | \node [style=none] (12) at (10.25, 0) {}; 12 | \node [style=none] (13) at (6, 0) {$=$}; 13 | \node [style=none] (15) at (12, 0) {$\leftrightsquigarrow$}; 14 | \node [style=none] (16) at (16.25, 0) {}; 15 | \node [style=box] (17) at (15, 0) {$I$}; 16 | \node [style=none] (18) at (13.75, 0) {}; 17 | \end{pgfonlayer} 18 | \begin{pgfonlayer}{edgelayer} 19 | \draw [style=simple] (4) to (5.center); 20 | \draw [style=simple] (4) to (1.center); 21 | \draw [style=simple] (8) to (9.center); 22 | \draw [style=simple] (8) to (7.center); 23 | \draw [style=simple] (10.center) to (12.center); 24 | \draw [style=simple] (17) to (18.center); 25 | \draw [style=simple] (17) to (16.center); 26 | \end{pgfonlayer} 27 | \end{tikzpicture} 28 | -------------------------------------------------------------------------------- /figures/zxXfusion1q.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=X phase dot] (0) at (-3.75, 1) {$\alpha$}; 4 | \node [style=none] (1) at (-1.5, 1) {}; 5 | \node [style=none] (2) at (0, 1) {$=$}; 6 | \node [style=X phase dot] (3) at (2.75, 1) {$\alpha+\beta$}; 7 | \node [style=none] (4) at (4.25, 1) {}; 8 | \node [style=X phase dot] (5) at (-2.5, 1) {$\beta$}; 9 | \node [style=X phase dot] (6) at (-3.75, 0) {$\alpha$}; 10 | \node [style=none] (8) at (0, 0) {$=$}; 11 | \node [style=X phase dot] (9) at (2.75, 0) {$\alpha+\beta$}; 12 | \node [style=X phase dot] (11) at (-2.5, 0) {$\beta$}; 13 | \node [style=none] (14) at (-4.75, 0) {}; 14 | \node [style=none] (19) at (1.25, 0) {}; 15 | \node [style=X phase dot] (20) at (-3.75, -1) {$\alpha$}; 16 | \node [style=none] (21) at (-1.5, -1) {}; 17 | \node [style=none] (22) at (0, -1) {$=$}; 18 | \node [style=X phase dot] (23) at (2.75, -1) {$\alpha+\beta$}; 19 | \node [style=none] (24) at (4.25, -1) {}; 20 | \node [style=X phase dot] (25) at (-2.5, -1) {$\beta$}; 21 | \node [style=none] (26) at (-4.75, -1) {}; 22 | \node [style=none] (27) at (1.25, -1) {}; 23 | \node [style=X phase dot] (28) at (-3.75, 2) {$\alpha$}; 24 | \node [style=none] (30) at (0, 2) {$=$}; 25 | \node [style=X phase dot] (31) at (2.75, 2) {$\alpha+\beta$}; 26 | \node [style=X phase dot] (33) at (-2.5, 2) {$\beta$}; 27 | \end{pgfonlayer} 28 | \begin{pgfonlayer}{edgelayer} 29 | \draw [style=simple] (3) to (4.center); 30 | \draw [style=simple] (0) to (5); 31 | \draw [style=simple] (5) to (1.center); 32 | \draw [style=simple] (6) to (11); 33 | \draw [style=simple] (14.center) to (6); 34 | \draw [style=simple] (19.center) to (9); 35 | \draw [style=simple] (23) to (24.center); 36 | \draw [style=simple] (20) to (25); 37 | \draw [style=simple] (25) to (21.center); 38 | \draw [style=simple] (26.center) to (20); 39 | \draw [style=simple] (27.center) to (23); 40 | \draw [style=simple] (28) to (33); 41 | \end{pgfonlayer} 42 | \end{tikzpicture} 43 | -------------------------------------------------------------------------------- /figures/zxXfusion1qff.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=X phase dot] (28) at (-3.75, 0) {$\alpha$}; 4 | \node [style=none] (30) at (0, 0) {$=$}; 5 | \node [style=X phase dot] (31) at (2.75, 0) {$\alpha+\beta$}; 6 | \node [style=X phase dot] (33) at (-2.5, 0) {$\beta$}; 7 | \end{pgfonlayer} 8 | \begin{pgfonlayer}{edgelayer} 9 | \draw [style=simple] (28) to (33); 10 | \end{pgfonlayer} 11 | \end{tikzpicture} 12 | -------------------------------------------------------------------------------- /figures/zxXfusion1qft.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=X phase dot] (0) at (-3.75, 0) {$\alpha$}; 4 | \node [style=none] (1) at (-1.5, 0) {}; 5 | \node [style=none] (2) at (0, 0) {$=$}; 6 | \node [style=X phase dot] (3) at (2.75, 0) {$\alpha+\beta$}; 7 | \node [style=none] (4) at (4.25, 0) {}; 8 | \node [style=X phase dot] (5) at (-2.5, 0) {$\beta$}; 9 | \end{pgfonlayer} 10 | \begin{pgfonlayer}{edgelayer} 11 | \draw [style=simple] (3) to (4.center); 12 | \draw [style=simple] (0) to (5); 13 | \draw [style=simple] (5) to (1.center); 14 | \end{pgfonlayer} 15 | \end{tikzpicture} 16 | -------------------------------------------------------------------------------- /figures/zxXfusion1qtf.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=X phase dot] (6) at (-3.75, 0) {$\alpha$}; 4 | \node [style=none] (7) at (0, 0) {$=$}; 5 | \node [style=X phase dot] (8) at (2.75, 0) {$\alpha+\beta$}; 6 | \node [style=X phase dot] (9) at (-2.5, 0) {$\beta$}; 7 | \node [style=none] (10) at (-4.75, 0) {}; 8 | \node [style=none] (11) at (1.25, 0) {}; 9 | \end{pgfonlayer} 10 | \begin{pgfonlayer}{edgelayer} 11 | \draw [style=simple] (6) to (9); 12 | \draw [style=simple] (10.center) to (6); 13 | \draw [style=simple] (11.center) to (8); 14 | \end{pgfonlayer} 15 | \end{tikzpicture} 16 | -------------------------------------------------------------------------------- /figures/zxXfusion1qtt.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=X phase dot] (0) at (-3.75, 0) {$\alpha$}; 4 | \node [style=none] (1) at (-1.5, 0) {}; 5 | \node [style=none] (2) at (0, 0) {$=$}; 6 | \node [style=X phase dot] (3) at (2.75, 0) {$\alpha+\beta$}; 7 | \node [style=none] (4) at (4.25, 0) {}; 8 | \node [style=X phase dot] (5) at (-2.5, 0) {$\beta$}; 9 | \node [style=none] (6) at (-4.75, 0) {}; 10 | \node [style=none] (7) at (1.25, 0) {}; 11 | \end{pgfonlayer} 12 | \begin{pgfonlayer}{edgelayer} 13 | \draw [style=simple] (3) to (4.center); 14 | \draw [style=simple] (0) to (5); 15 | \draw [style=simple] (5) to (1.center); 16 | \draw [style=simple] (6.center) to (0); 17 | \draw [style=simple] (7.center) to (3); 18 | \end{pgfonlayer} 19 | \end{tikzpicture} 20 | -------------------------------------------------------------------------------- /figures/zxXk0.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=X dot] (0) at (-3.75, 0) {}; 4 | \node [style=none] (1) at (-1.5, 0) {}; 5 | \node [style=none] (2) at (0, 0) {$=$}; 6 | \node [style=X phase dot] (3) at (1.75, 0) {$\pi$}; 7 | \node [style=none] (4) at (3.25, 0) {}; 8 | \node [style=X phase dot] (5) at (-2.5, 0) {$\pi$}; 9 | \end{pgfonlayer} 10 | \begin{pgfonlayer}{edgelayer} 11 | \draw [style=simple] (3) to (4.center); 12 | \draw [style=simple] (0) to (5); 13 | \draw [style=simple] (5) to (1.center); 14 | \end{pgfonlayer} 15 | \end{tikzpicture} 16 | -------------------------------------------------------------------------------- /figures/zxXk1.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=X phase dot] (0) at (-3.75, 0) {$\pi$}; 4 | \node [style=none] (1) at (-1.5, 0) {}; 5 | \node [style=none] (2) at (0, 0) {$=$}; 6 | \node [style=X phase dot] (3) at (1.75, 0) {$2\pi$}; 7 | \node [style=none] (4) at (3.25, 0) {}; 8 | \node [style=X phase dot] (5) at (-2.5, 0) {$\pi$}; 9 | \node [style=none] (6) at (4.75, 0) {$=$}; 10 | \node [style=X dot] (7) at (6.5, 0) {}; 11 | \node [style=none] (8) at (8, 0) {}; 12 | \end{pgfonlayer} 13 | \begin{pgfonlayer}{edgelayer} 14 | \draw [style=simple] (3) to (4.center); 15 | \draw [style=simple] (0) to (5); 16 | \draw [style=simple] (5) to (1.center); 17 | \draw [style=simple] (7) to (8.center); 18 | \end{pgfonlayer} 19 | \end{tikzpicture} 20 | -------------------------------------------------------------------------------- /figures/zxXphase.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=none] (1) at (-1.75, 0) {}; 4 | \node [style=X phase dot] (4) at (-3, 0) {$\alpha$}; 5 | \node [style=none] (5) at (-4.25, 0) {}; 6 | \node [style=none] (9) at (0, 0) {$\coloneqq$}; 7 | \node [style=none] (10) at (2, 0) {$X(\alpha)$}; 8 | \end{pgfonlayer} 9 | \begin{pgfonlayer}{edgelayer} 10 | \draw [style=simple] (4) to (5.center); 11 | \draw [style=simple] (4) to (1.center); 12 | \end{pgfonlayer} 13 | \end{tikzpicture} 14 | -------------------------------------------------------------------------------- /figures/zxZ.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=none] (2) at (0, 0) {$\leftrightsquigarrow$}; 4 | \node [style=none] (9) at (1.75, 0) {}; 5 | \node [style=box] (10) at (3, 0) {$Z$}; 6 | \node [style=none] (11) at (4.25, 0) {}; 7 | \node [style=none] (12) at (-4.25, 0) {}; 8 | \node [style=Z phase dot] (13) at (-3, 0) {$\pi$}; 9 | \node [style=none] (14) at (-1.75, 0) {}; 10 | \end{pgfonlayer} 11 | \begin{pgfonlayer}{edgelayer} 12 | \draw [style=simple] (10) to (11.center); 13 | \draw [style=simple] (10) to (9.center); 14 | \draw [style=simple] (13) to (14.center); 15 | \draw [style=simple] (13) to (12.center); 16 | \end{pgfonlayer} 17 | \end{tikzpicture} 18 | -------------------------------------------------------------------------------- /figures/zxZI.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=none] (1) at (-1.75, 0) {}; 4 | \node [style=Z dot] (4) at (-3, 0) {}; 5 | \node [style=none] (5) at (-4.25, 0) {}; 6 | \node [style=none] (6) at (0, 0) {$=$}; 7 | \node [style=none] (7) at (4.25, 0) {}; 8 | \node [style=Z phase dot] (8) at (3, 0) {0}; 9 | \node [style=none] (9) at (1.75, 0) {}; 10 | \node [style=none] (10) at (7.75, 0) {}; 11 | \node [style=none] (12) at (10.25, 0) {}; 12 | \node [style=none] (13) at (6, 0) {$=$}; 13 | \node [style=none] (27) at (12, 0) {$\leftrightsquigarrow$}; 14 | \node [style=none] (28) at (16.25, 0) {}; 15 | \node [style=box] (29) at (15, 0) {$I$}; 16 | \node [style=none] (30) at (13.75, 0) {}; 17 | \end{pgfonlayer} 18 | \begin{pgfonlayer}{edgelayer} 19 | \draw [style=simple] (4) to (5.center); 20 | \draw [style=simple] (4) to (1.center); 21 | \draw [style=simple] (8) to (9.center); 22 | \draw [style=simple] (8) to (7.center); 23 | \draw [style=simple] (10.center) to (12.center); 24 | \draw [style=simple] (29) to (30.center); 25 | \draw [style=simple] (29) to (28.center); 26 | \end{pgfonlayer} 27 | \end{tikzpicture} 28 | -------------------------------------------------------------------------------- /figures/zxZXI.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=none] (1) at (-4.75, 0) {}; 4 | \node [style=Z dot] (4) at (-6, 0) {}; 5 | \node [style=none] (5) at (-7.25, 0) {}; 6 | \node [style=none] (6) at (-3, 0) {$=$}; 7 | \node [style=none] (10) at (-1.25, 0) {}; 8 | \node [style=none] (12) at (1.25, 0) {}; 9 | \node [style=none] (13) at (4.75, 0) {}; 10 | \node [style=X dot] (14) at (6, 0) {}; 11 | \node [style=none] (15) at (7.25, 0) {}; 12 | \node [style=none] (16) at (3, 0) {$=$}; 13 | \end{pgfonlayer} 14 | \begin{pgfonlayer}{edgelayer} 15 | \draw [style=simple] (4) to (5.center); 16 | \draw [style=simple] (4) to (1.center); 17 | \draw [style=simple] (10.center) to (12.center); 18 | \draw [style=simple] (14) to (15.center); 19 | \draw [style=simple] (14) to (13.center); 20 | \end{pgfonlayer} 21 | \end{tikzpicture} 22 | -------------------------------------------------------------------------------- /figures/zxZfusion1qff.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=Z phase dot] (28) at (-3.75, 0) {$\alpha$}; 4 | \node [style=none] (30) at (0, 0) {$=$}; 5 | \node [style=Z phase dot] (31) at (2.75, 0) {$\alpha+\beta$}; 6 | \node [style=Z phase dot] (33) at (-2.5, 0) {$\beta$}; 7 | \end{pgfonlayer} 8 | \begin{pgfonlayer}{edgelayer} 9 | \draw [style=simple] (28) to (33); 10 | \end{pgfonlayer} 11 | \end{tikzpicture} 12 | -------------------------------------------------------------------------------- /figures/zxZfusion1qft.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=Z phase dot] (0) at (-3.75, 0) {$\alpha$}; 4 | \node [style=none] (1) at (-1.5, 0) {}; 5 | \node [style=none] (2) at (0, 0) {$=$}; 6 | \node [style=Z phase dot] (3) at (2.75, 0) {$\alpha+\beta$}; 7 | \node [style=none] (4) at (4.25, 0) {}; 8 | \node [style=Z phase dot] (5) at (-2.5, 0) {$\beta$}; 9 | \end{pgfonlayer} 10 | \begin{pgfonlayer}{edgelayer} 11 | \draw [style=simple] (3) to (4.center); 12 | \draw [style=simple] (0) to (5); 13 | \draw [style=simple] (5) to (1.center); 14 | \end{pgfonlayer} 15 | \end{tikzpicture} 16 | -------------------------------------------------------------------------------- /figures/zxZfusion1qstate.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=Z dot] (28) at (-3.25, 0) {}; 4 | \node [style=none] (30) at (0, 0) {$=$}; 5 | \node [style=Z phase dot] (33) at (-2.25, 0) {$\gamma$}; 6 | \node [style=none] (34) at (-1.25, 0) {}; 7 | \node [style=Z phase dot] (35) at (1.75, 0) {$\gamma$}; 8 | \node [style=none] (36) at (3.25, 0) {}; 9 | \end{pgfonlayer} 10 | \begin{pgfonlayer}{edgelayer} 11 | \draw [style=simple] (28) to (33); 12 | \draw [style=simple] (34.center) to (33); 13 | \draw [style=simple] (36.center) to (35); 14 | \end{pgfonlayer} 15 | \end{tikzpicture} 16 | -------------------------------------------------------------------------------- /figures/zxZfusion1qstatetest.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=none] (30) at (0, 0) {$=$}; 4 | \node [style=Z phase dot] (33) at (2, 0) {$\gamma$}; 5 | \node [style=Z dot] (37) at (-3.5, 0) {}; 6 | \node [style=Z phase dot] (39) at (-2.5, 0) {$\gamma$}; 7 | \node [style=Z dot] (40) at (-1.5, 0) {}; 8 | \end{pgfonlayer} 9 | \begin{pgfonlayer}{edgelayer} 10 | \draw [style=simple] (37) to (39); 11 | \draw [style=simple] (40) to (39); 12 | \end{pgfonlayer} 13 | \end{tikzpicture} 14 | -------------------------------------------------------------------------------- /figures/zxZfusion1qtest.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=none] (30) at (0, 0) {$=$}; 4 | \node [style=Z dot] (37) at (-1.25, 0) {}; 5 | \node [style=Z phase dot] (38) at (-2.25, 0) {$\gamma$}; 6 | \node [style=none] (39) at (-3.25, 0) {}; 7 | \node [style=Z phase dot] (40) at (2.75, 0) {$\gamma$}; 8 | \node [style=none] (41) at (1.25, 0) {}; 9 | \end{pgfonlayer} 10 | \begin{pgfonlayer}{edgelayer} 11 | \draw [style=simple] (37) to (38); 12 | \draw [style=simple] (39.center) to (38); 13 | \draw [style=simple] (41.center) to (40); 14 | \end{pgfonlayer} 15 | \end{tikzpicture} 16 | -------------------------------------------------------------------------------- /figures/zxZfusion1qtf.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=Z phase dot] (6) at (-3.75, 0) {$\alpha$}; 4 | \node [style=none] (7) at (0, 0) {$=$}; 5 | \node [style=Z phase dot] (8) at (2.75, 0) {$\alpha+\beta$}; 6 | \node [style=Z phase dot] (9) at (-2.5, 0) {$\beta$}; 7 | \node [style=none] (10) at (-4.75, 0) {}; 8 | \node [style=none] (11) at (1.25, 0) {}; 9 | \end{pgfonlayer} 10 | \begin{pgfonlayer}{edgelayer} 11 | \draw [style=simple] (6) to (9); 12 | \draw [style=simple] (10.center) to (6); 13 | \draw [style=simple] (11.center) to (8); 14 | \end{pgfonlayer} 15 | \end{tikzpicture} 16 | -------------------------------------------------------------------------------- /figures/zxZfusion1qtt.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=Z phase dot] (0) at (-3.75, 0) {$\alpha$}; 4 | \node [style=none] (1) at (-1.5, 0) {}; 5 | \node [style=none] (2) at (0, 0) {$=$}; 6 | \node [style=Z phase dot] (3) at (2.75, 0) {$\alpha+\beta$}; 7 | \node [style=none] (4) at (4.25, 0) {}; 8 | \node [style=Z phase dot] (5) at (-2.5, 0) {$\beta$}; 9 | \node [style=none] (6) at (-4.75, 0) {}; 10 | \node [style=none] (7) at (1.25, 0) {}; 11 | \end{pgfonlayer} 12 | \begin{pgfonlayer}{edgelayer} 13 | \draw [style=simple] (3) to (4.center); 14 | \draw [style=simple] (0) to (5); 15 | \draw [style=simple] (5) to (1.center); 16 | \draw [style=simple] (6.center) to (0); 17 | \draw [style=simple] (7.center) to (3); 18 | \end{pgfonlayer} 19 | \end{tikzpicture} 20 | -------------------------------------------------------------------------------- /figures/zxZk+.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=Z dot] (0) at (-3.75, 0) {}; 4 | \node [style=none] (1) at (-1.5, 0) {}; 5 | \node [style=none] (2) at (0, 0) {$=$}; 6 | \node [style=Z phase dot] (3) at (1.75, 0) {$\pi$}; 7 | \node [style=none] (4) at (3.25, 0) {}; 8 | \node [style=Z phase dot] (5) at (-2.5, 0) {$\pi$}; 9 | \end{pgfonlayer} 10 | \begin{pgfonlayer}{edgelayer} 11 | \draw [style=simple] (3) to (4.center); 12 | \draw [style=simple] (0) to (5); 13 | \draw [style=simple] (5) to (1.center); 14 | \end{pgfonlayer} 15 | \end{tikzpicture} 16 | -------------------------------------------------------------------------------- /figures/zxZk-.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=Z phase dot] (0) at (-3.75, 0) {$\pi$}; 4 | \node [style=none] (1) at (-1.5, 0) {}; 5 | \node [style=none] (2) at (0, 0) {$=$}; 6 | \node [style=Z phase dot] (3) at (1.75, 0) {$2\pi$}; 7 | \node [style=none] (4) at (3.25, 0) {}; 8 | \node [style=Z phase dot] (5) at (-2.5, 0) {$\pi$}; 9 | \node [style=none] (7) at (4.75, 0) {$=$}; 10 | \node [style=Z dot] (8) at (6.5, 0) {}; 11 | \node [style=none] (9) at (8, 0) {}; 12 | \end{pgfonlayer} 13 | \begin{pgfonlayer}{edgelayer} 14 | \draw [style=simple] (3) to (4.center); 15 | \draw [style=simple] (0) to (5); 16 | \draw [style=simple] (5) to (1.center); 17 | \draw [style=simple] (8) to (9.center); 18 | \end{pgfonlayer} 19 | \end{tikzpicture} 20 | -------------------------------------------------------------------------------- /figures/zxZphase.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=none] (1) at (-1.75, 0) {}; 4 | \node [style=Z phase dot] (4) at (-3, 0) {$\alpha$}; 5 | \node [style=none] (5) at (-4.25, 0) {}; 6 | \node [style=none] (8) at (0, 0) {$\coloneqq$}; 7 | \node [style=none] (9) at (2, 0) {$Z(\alpha)$}; 8 | \end{pgfonlayer} 9 | \begin{pgfonlayer}{edgelayer} 10 | \draw [style=simple] (4) to (5.center); 11 | \draw [style=simple] (4) to (1.center); 12 | \end{pgfonlayer} 13 | \end{tikzpicture} 14 | -------------------------------------------------------------------------------- /figures/zxbialgebracopy.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=Z dot] (22) at (-3, 0) {}; 4 | \node [style=none] (24) at (-1.75, 1) {}; 5 | \node [style=X dot] (26) at (-4.5, 0) {}; 6 | \node [style=none] (27) at (-1.75, -1) {}; 7 | \node [style=none] (28) at (0, 0) {$=$}; 8 | \node [style=none] (29) at (3.75, 1) {}; 9 | \node [style=none] (30) at (3.75, -1) {}; 10 | \node [style=X dot] (31) at (2, 1) {}; 11 | \node [style=X dot] (32) at (2, -1) {}; 12 | \end{pgfonlayer} 13 | \begin{pgfonlayer}{edgelayer} 14 | \draw [style=simple] (26) to (22); 15 | \draw [style=simple] (22) to (24.center); 16 | \draw [style=simple] (27.center) to (22); 17 | \draw [style=simple] (31) to (29.center); 18 | \draw [style=simple] (30.center) to (32); 19 | \end{pgfonlayer} 20 | \end{tikzpicture} 21 | -------------------------------------------------------------------------------- /figures/zxbialgebracopyapi.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=Z dot] (22) at (-3, 0) {}; 4 | \node [style=none] (24) at (-1.75, 1) {}; 5 | \node [style=X phase dot] (26) at (-4.5, 0) {$a\pi$}; 6 | \node [style=none] (27) at (-1.75, -1) {}; 7 | \node [style=none] (28) at (0, 0) {$=$}; 8 | \node [style=none] (29) at (3.75, 1) {}; 9 | \node [style=none] (30) at (3.75, -1) {}; 10 | \node [style=X phase dot] (31) at (2, 1) {$a\pi$}; 11 | \node [style=X phase dot] (32) at (2, -1) {$a\pi$}; 12 | \end{pgfonlayer} 13 | \begin{pgfonlayer}{edgelayer} 14 | \draw [style=simple] (26) to (22); 15 | \draw [style=simple] (22) to (24.center); 16 | \draw [style=simple] (27.center) to (22); 17 | \draw [style=simple] (31) to (29.center); 18 | \draw [style=simple] (30.center) to (32); 19 | \end{pgfonlayer} 20 | \end{tikzpicture} 21 | -------------------------------------------------------------------------------- /figures/zxbialgebracopyapiT.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=Z dot] (22) at (-3.25, 0) {}; 4 | \node [style=none] (24) at (-4.5, 1) {}; 5 | \node [style=X phase dot] (26) at (-1.75, 0) {$a\pi$}; 6 | \node [style=none] (27) at (-4.5, -1) {}; 7 | \node [style=none] (28) at (0, 0) {$=$}; 8 | \node [style=none] (29) at (2, 1) {}; 9 | \node [style=none] (30) at (2, -1) {}; 10 | \node [style=X phase dot] (31) at (3.75, 1) {$a\pi$}; 11 | \node [style=X phase dot] (32) at (3.75, -1) {$a\pi$}; 12 | \end{pgfonlayer} 13 | \begin{pgfonlayer}{edgelayer} 14 | \draw [style=simple] (26) to (22); 15 | \draw [style=simple] (22) to (24.center); 16 | \draw [style=simple] (27.center) to (22); 17 | \draw [style=simple] (31) to (29.center); 18 | \draw [style=simple] (30.center) to (32); 19 | \end{pgfonlayer} 20 | \end{tikzpicture} 21 | -------------------------------------------------------------------------------- /figures/zxbialgebracopyapih.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=X dot] (22) at (-3, 0) {}; 4 | \node [style=none] (24) at (-1.75, 1) {}; 5 | \node [style=Z phase dot] (26) at (-4.5, 0) {$a\pi$}; 6 | \node [style=none] (27) at (-1.75, -1) {}; 7 | \node [style=none] (28) at (0, 0) {$=$}; 8 | \node [style=none] (33) at (0, -10.5) {$=$}; 9 | \node [style=none] (34) at (3.75, -9.75) {}; 10 | \node [style=none] (35) at (3.75, -11.5) {}; 11 | \node [style=Z phase dot] (36) at (1.75, -9.75) {$a\pi$}; 12 | \node [style=Z phase dot] (37) at (1.75, -11.5) {$a\pi$}; 13 | \node [style=Z dot] (38) at (3.25, 0) {}; 14 | \node [style=none] (39) at (4.5, 1) {}; 15 | \node [style=Z phase dot] (40) at (1.75, 0) {$a\pi$}; 16 | \node [style=none] (41) at (4.5, -1) {}; 17 | \node [style=hadamard] (42) at (4, 0.625) {}; 18 | \node [style=hadamard] (43) at (4, -0.6) {}; 19 | \node [style=hadamard] (44) at (2.5, 0) {}; 20 | \node [style=none] (45) at (0, -3.5) {$=$}; 21 | \node [style=Z dot] (46) at (3.25, -3.5) {}; 22 | \node [style=none] (47) at (4.5, -2.5) {}; 23 | \node [style=X phase dot] (48) at (1.75, -3.5) {$a\pi$}; 24 | \node [style=none] (49) at (4.5, -4.5) {}; 25 | \node [style=hadamard] (50) at (4, -2.875) {}; 26 | \node [style=hadamard] (51) at (4, -4.1) {}; 27 | \node [style=none] (52) at (0, -6.75) {$=$}; 28 | \node [style=none] (53) at (3.75, -6) {}; 29 | \node [style=none] (54) at (3.75, -7.75) {}; 30 | \node [style=X phase dot] (55) at (1.75, -6) {$a\pi$}; 31 | \node [style=X phase dot] (56) at (1.75, -7.75) {$a\pi$}; 32 | \node [style=hadamard] (57) at (2.75, -6) {}; 33 | \node [style=hadamard] (58) at (2.75, -7.75) {}; 34 | \end{pgfonlayer} 35 | \begin{pgfonlayer}{edgelayer} 36 | \draw [style=simple] (26) to (22); 37 | \draw [style=simple] (22) to (24.center); 38 | \draw [style=simple] (27.center) to (22); 39 | \draw [style=simple] (36) to (34.center); 40 | \draw [style=simple] (35.center) to (37); 41 | \draw [style=simple] (40) to (44); 42 | \draw [style=simple] (44) to (38); 43 | \draw [style=simple] (38) to (42); 44 | \draw [style=simple] (42) to (39.center); 45 | \draw [style=simple] (41.center) to (43); 46 | \draw [style=simple] (43) to (38); 47 | \draw [style=simple] (46) to (50); 48 | \draw [style=simple] (50) to (47.center); 49 | \draw [style=simple] (49.center) to (51); 50 | \draw [style=simple] (51) to (46); 51 | \draw [style=simple] (48) to (46); 52 | \draw [style=simple] (55) to (57); 53 | \draw [style=simple] (57) to (53.center); 54 | \draw [style=simple] (54.center) to (58); 55 | \draw [style=simple] (58) to (56); 56 | \end{pgfonlayer} 57 | \end{tikzpicture} 58 | -------------------------------------------------------------------------------- /figures/zxbialgebracopyapioppcolor.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=X dot] (22) at (-3, 0) {}; 4 | \node [style=none] (24) at (-1.75, 1) {}; 5 | \node [style=Z phase dot] (26) at (-4.5, 0) {$a\pi$}; 6 | \node [style=none] (27) at (-1.75, -1) {}; 7 | \node [style=none] (28) at (0, 0) {$=$}; 8 | \node [style=none] (29) at (3.75, 1) {}; 9 | \node [style=none] (30) at (3.75, -1) {}; 10 | \node [style=Z phase dot] (31) at (2, 1) {$a\pi$}; 11 | \node [style=Z phase dot] (32) at (2, -1) {$a\pi$}; 12 | \end{pgfonlayer} 13 | \begin{pgfonlayer}{edgelayer} 14 | \draw [style=simple] (26) to (22); 15 | \draw [style=simple] (22) to (24.center); 16 | \draw [style=simple] (27.center) to (22); 17 | \draw [style=simple] (31) to (29.center); 18 | \draw [style=simple] (30.center) to (32); 19 | \end{pgfonlayer} 20 | \end{tikzpicture} 21 | -------------------------------------------------------------------------------- /figures/zxbialgebracopyapioppcolorT.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=X dot] (22) at (-3.25, 0) {}; 4 | \node [style=none] (24) at (-4.5, 1) {}; 5 | \node [style=Z phase dot] (26) at (-1.75, 0) {$a\pi$}; 6 | \node [style=none] (27) at (-4.5, -1) {}; 7 | \node [style=none] (28) at (0, 0) {$=$}; 8 | \node [style=none] (29) at (2, 1) {}; 9 | \node [style=none] (30) at (2, -1) {}; 10 | \node [style=Z phase dot] (31) at (3.75, 1) {$a\pi$}; 11 | \node [style=Z phase dot] (32) at (3.75, -1) {$a\pi$}; 12 | \end{pgfonlayer} 13 | \begin{pgfonlayer}{edgelayer} 14 | \draw [style=simple] (26) to (22); 15 | \draw [style=simple] (22) to (24.center); 16 | \draw [style=simple] (27.center) to (22); 17 | \draw [style=simple] (31) to (29.center); 18 | \draw [style=simple] (30.center) to (32); 19 | \end{pgfonlayer} 20 | \end{tikzpicture} 21 | -------------------------------------------------------------------------------- /figures/zxbialgebracopypi.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=Z dot] (22) at (-3, 0) {}; 4 | \node [style=none] (24) at (-1.75, 1) {}; 5 | \node [style=X phase dot] (26) at (-4.5, 0) {$\pi$}; 6 | \node [style=none] (27) at (-1.75, -1) {}; 7 | \node [style=none] (28) at (0, 0) {$=$}; 8 | \node [style=none] (29) at (3.75, 1) {}; 9 | \node [style=none] (30) at (3.75, -1) {}; 10 | \node [style=X phase dot] (31) at (2, 1) {$\pi$}; 11 | \node [style=X phase dot] (32) at (2, -1) {$\pi$}; 12 | \end{pgfonlayer} 13 | \begin{pgfonlayer}{edgelayer} 14 | \draw [style=simple] (26) to (22); 15 | \draw [style=simple] (22) to (24.center); 16 | \draw [style=simple] (27.center) to (22); 17 | \draw [style=simple] (31) to (29.center); 18 | \draw [style=simple] (30.center) to (32); 19 | \end{pgfonlayer} 20 | \end{tikzpicture} 21 | -------------------------------------------------------------------------------- /figures/zxcolorchange.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=none] (2) at (0, 0) {$=$}; 4 | \node [style=none] (9) at (-1.75, 0) {}; 5 | \node [style=Z phase dot] (10) at (-3.25, 0) {$\alpha$}; 6 | \node [style=none] (11) at (-4.75, 0) {}; 7 | \node [style=X phase dot] (12) at (5, 0) {$\alpha$}; 8 | \node [style=hadamard] (13) at (3, 0) {}; 9 | \node [style=none] (14) at (1.75, 0) {}; 10 | \node [style=hadamard] (16) at (7, 0) {}; 11 | \node [style=none] (17) at (8.25, 0) {}; 12 | \end{pgfonlayer} 13 | \begin{pgfonlayer}{edgelayer} 14 | \draw [style=simple] (10) to (11.center); 15 | \draw [style=simple] (10) to (9.center); 16 | \draw [style=simple] (13) to (14.center); 17 | \draw [style=simple] (13) to (12); 18 | \draw [style=simple] (16) to (17.center); 19 | \draw [style=simple] (16) to (12); 20 | \end{pgfonlayer} 21 | \end{tikzpicture} 22 | -------------------------------------------------------------------------------- /figures/zxcommuteHX.tikz: -------------------------------------------------------------------------------- 1 | \begin{tikzpicture} 2 | \begin{pgfonlayer}{nodelayer} 3 | \node [style=none] (2) at (0, 4) {$\leftrightsquigarrow$}; 4 | \node [style=box] (12) at (-3, 4) {$X$}; 5 | \node [style=none] (14) at (-1.75, 4) {}; 6 | \node [style=box] (16) at (-4.75, 4) {$H$}; 7 | \node [style=none] (17) at (-6, 4) {}; 8 | \node [style=X phase dot] (18) at (4.25, 2) {$\pi$}; 9 | \node [style=hadamard] (19) at (5.5, 2) {}; 10 | \node [style=hadamard] (20) at (3, 2) {}; 11 | \node [style=none] (21) at (1.75, 2) {}; 12 | \node [style=none] (23) at (8, 2) {}; 13 | \node [style=hadamard] (24) at (6.75, 2) {}; 14 | \node [style=X phase dot] (25) at (4.25, 4) {$\pi$}; 15 | \node [style=none] (26) at (8, 4) {}; 16 | \node [style=hadamard] (27) at (3, 4) {}; 17 | \node [style=none] (28) at (1.75, 4) {}; 18 | \node [style=none] (29) at (5, 3) {$\rotatebox{90}{=}$}; 19 | \node [style=Z phase dot] (30) at (4.25, 0) {$\pi$}; 20 | \node [style=none] (33) at (1.75, 0) {}; 21 | \node [style=none] (34) at (8, 0) {}; 22 | \node [style=hadamard] (35) at (6.75, 0) {}; 23 | \node [style=none] (37) at (0, 0) {$\leftrightsquigarrow$}; 24 | \node [style=box] (38) at (-4.75, 0) {$Z$}; 25 | \node [style=none] (39) at (-6, 0) {}; 26 | \node [style=box] (40) at (-3, 0) {$H$}; 27 | \node [style=none] (41) at (-1.75, 0) {}; 28 | \node [style=none] (42) at (5, 1) {$\rotatebox{90}{=}$}; 29 | \node [style=none] (43) at (5.125, 4.5) {}; 30 | \node [style=none] (44) at (7.125, 4.5) {}; 31 | \node [style=none] (45) at (7.125, 3.5) {}; 32 | \node [style=none] (46) at (5.125, 3.5) {}; 33 | \node [style=none] (47) at (2.625, 2.5) {}; 34 | \node [style=none] (48) at (5.875, 2.5) {}; 35 | \node [style=none] (49) at (5.875, 1.5) {}; 36 | \node [style=none] (50) at (2.625, 1.5) {}; 37 | \node [style=none] (51) at (-3.825, 2) {$\rotatebox{90}{=}$}; 38 | \end{pgfonlayer} 39 | \begin{pgfonlayer}{edgelayer} 40 | \draw [style=simple] (16) to (17.center); 41 | \draw [style=simple] (16) to (12); 42 | \draw [style=simple] (12) to (14.center); 43 | \draw [style=simple] (20) to (21.center); 44 | \draw [style=simple] (20) to (18); 45 | \draw [style=simple] (18) to (19); 46 | \draw [style=simple] (19) to (24); 47 | \draw [style=simple] (24) to (23.center); 48 | \draw [style=simple] (27) to (28.center); 49 | \draw [style=simple] (27) to (25); 50 | \draw [style=simple] (25) to (26.center); 51 | \draw [style=simple] (35) to (34.center); 52 | \draw [style=simple] (33.center) to (30); 53 | \draw [style=simple] (30) to (35); 54 | \draw [style=simple] (40) to (41.center); 55 | \draw [style=simple] (40) to (38); 56 | \draw [style=simple] (38) to (39.center); 57 | \draw [style=dashed gray 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