Wn | WikiNames | WikiPict | WikiPictAlt | Qn | QuosName1 | QuosName2 | QuosPict1 | QuosPict2 | Qubits | MatrixString |
1 | I, Identity, No-op |  |  | 1 | I | |  | | 1 | |1 0|0 1 |
2 | Ph, Phase, (e^id)I, Global phase |  | | 2 | Ph | |  | | 1 | e^id|1 0|0 1 |
3 | X, Pauli X, sx, NOT, Bit flip |  |  | 3 | X | |  | | 1 | |0 1|1 0 |
4 | Y, Pauli Y, sy |  | | 4 | Y | |  | | 1 | |0 -i|i 0 |
5 | Z, Pauli Z, sz, Phase flip |  | | 5 | Z | |  | | 1 | |1 0|0 -1 |
6 | S, sqrt-Z, P, Phase S |  | | 6 | S | |  | | 1 | |1 0|0 i |
7 | V, sqrt-X, sqrt-NOT, SX |  | | 7 | V | |  | | 1 | 1/2|1+i 1-i|1-i 1+i |
8 | H, Hadamard, Walsh-Hadamard |  | | 8 | H | |  | | 1 | 1/sqrt2|1 1|1 -1 |
9 | CX, CNOT, XOR, Controlled NOT, Controlled X, Reversible exclusive OR, Feynman |  | | 9 | C | X |  |  | 2 | |1 0 0 0|0 1 0 0|0 0 0 1|0 0 1 0 |
10 | CdX, CdashX, XNOR, Controlled NOT, Anticontrolled X, Zero control, Control-on-0-NOT, Reversible exclusive NOR |  | | 10 | Cd | X |  |  | 2 | |0 1 0 0|1 0 0 0|0 0 1 0|0 0 0 1 |
11 | CZ, CPF, CSign, Cphase, Controlled Z, Controlled sign flip, Controlled phase flip |  | | 11 | C | Z |  |  | 2 | |1 0 0 0|0 1 0 0|0 0 1 0|0 0 0 -1 |
12 | Double-controlled NOT , DCNOT |  | | | | | | | 2 | |1 0 0 0|0 0 1 0|0 0 0 1|0 1 0 0 |
13 | Swap |  |  | 12 | Sw | Sw |  |  | 2 | |1 0 0 0|0 0 1 0|0 1 0 0|0 0 0 1 |
14 | iSwap, Imaginary swap |  |  | 13 | iSw | iSw |  |  | 2 | |1 0 0 0|0 0 i 0|0 i 0 0|0 0 0 1 |
15 | Pphi, P phi, R phi, u1 phi, Phase shift |  | | 14 | Pp | |  | | 1 | |1 0|0 e^if |
16 | T, Phase gate T, Pi/8 gate, P pi/4, Fourth root of Z |  | | 15 | T | |  | | 1 | |1 0|0 e^ip/4 |
17 | Controlled phase, C phase f, CR f |  | | 16 | C | Pp |  |  | 2 | |1 0 0 0|0 1 0 0|0 0 1 0|0 0 0 e^if |
18 | CS, Cntrolled S, Controlled phase S |  | | 17 | C | S |  |  | 2 | |1 0 0 0|0 1 0 0|0 0 1 0|0 0 0 i |
19 | Rx, Rx ?, Rotation about x-axis |  | | 18 | Rx | |  | | 1 | |cos?/2 -isin?/2|-isin?/2 cos?/2 |
20 | Ry, Ry ?. Rotation about y-axis |  | | 19 | Ry | |  | | 1 | |cos?/2 -sin?/2|sin?/2 cos?/2 |
21 | Rz, Rz ?. Rotation about z-axis |  | | 20 | Rz | |  | | 1 | |e^-i?/2 0|0 e^i?/2 |
22 | XX interaction, Rxx ?, XX ? | | | | | | | | 2 | |cos?/2 0 0 -isin?/2|0 cos?/2 -isin?/2 0|0 -isin?/2 cos?/2 0|-isin?/2 0 0 cos?/2 |
23 | YY interaction, Ryy ?, YY ? | | | | | | | | 2 | |cos?/2 0 0 isin?/2|0 cos?/2 -isin?/2 0|0 -isin?/2 cos?/2 0|isin?/2 0 0 cos?/2 |
24 | ZZ interaction, Rzz ?, ZZ ? | | | | | | | | 2 | |e^-i?/2 0 0 0|0 e^-i?/2 0 0|0 0 e^-i?/2 0|0 0 0 e^-i?/2 |
25 | XY, XX plus YY, Rxy ?, XY ? | | | | | | | | 2 | |1 0 0 0|0 cos?/2 -isin?/2 0|0 -isin?/2 cos?/2 0|0 0 0 1 |
26 | Square root swap |  | | | | | | | 2 | |1 0 0 0|0 (1+i)/2 (1-i)/2 0|0 (1-i)/2 (1+i)/2 0|0 0 0 1 |
27 | Square root imaginary swap | | | | | | | | 2 | |1 0 0 0|0 1/sqrt2 i/sqrt2 0|0 i/sqrt2 1/sqrt2 0|0 0 0 1 |
28 | Swap (raised to a power) |  | | | | | | | 2 | |1 0 0 0|0 (1+e^ipa)/2 (1-e^ipa)/2 0|0 (1-e^ipa)/2 (1+e^ipa)/2 0|0 0 0 1 |
29 | CSwap, Controlled swap, Fredkin |  |  | | | | | | 3 | |1 0 0 0 0 0 0 0|0 1 0 0 0 0 0 0|0 0 1 0 0 0 0 0|0 0 0 1 0 0 0 0|0 0 0 0 1 0 0 0|0 0 0 0 0 0 1 0|0 0 0 0 0 1 0 0|0 0 0 0 0 0 0 1 |
30 | General single qubit rotation, U ? ? ? | | | | | | | | 1 | |cos?/2 -(e^-i?)sin?/2 (e^-i?)sin?/2 (e^i(?+?))cos?/2 |
31 | Barenco, Barenco a ? ? | | | | | | | | 2 | |1 0 0 0|0 1 0 0|0 0 (e^ia)cos? ? -i(e^i(a-?)sin?|0 0 -i(e^i(a+?))sin? ? (e^ia)cos?? |
32 | B, Berkeley B | | | | | | | | 2 | |cosp/8 0 0 isinp/8|0 cos3p/8 isin3p/8 0|0 isinp/8 cosp/8 0|isinp/8 0 0 cosp/8 |
33 | CSX, controlled square root NOT, controlled square root X, Controlled V | | | | | | | | 2 | |1 0 0 0|0 1 0 0|0 0 e^ip/4 e^-ip/4|0 0 e^-ip/4 e^ip/4 |
34 | Core entangling, Canonical decomposition, N a b c, Can a b c | | | | | | | | 2 | |(e^ic)cos? (a-b) 0 0 (e^ic)sina-b)|0 (e^-ic)cos? (a+b) (e^-ic)sin? (a+b) 0|0 (e^-ic)sin? (a+b) (e^-ic)cos? (a+b) 0|(e^ic)sin? (a-b) 0 0 (e^ic)cos? (a-b) |
35 | Dagwood Bumstead, DB | | | | | | | | 2 | |1 0 0 0|0 cos3p/8 -isin3p/8 0|0 -isin3p/8 cos3p/8 0|0 0 0 1 |
36 | Echoed cross resonance, ECR | | | | | | | | 2 | 1/sqrt2|0 0 1 i|0 0 i 1|1 -i 0 0|-i 1 0 0 |
37 | Fermionic simulation, UfSim ? ?, fSim ? ? | | | | | | | | 2 | |1 0 0 0|0 cos? -isin? 0|0 -isin? cos? 0|0 0 0 e^i? |
38 | Givens. G ?, Givens ? | | | | | | | | 2 | |1 0 0 0|0 cos? -sin? 0|0 sin? cos? 0|0 0 0 1 |
39 | Magic. Mu | | | | | | | | 2 | 1/sqrt2|1 i 0 0|0 0 i 1|0 0 i -1|1 -i 0 0 |
40 | Sycamore, Syc, fSim p/2 p/6 | | | | | | | | 2 | |1 0 0 0|0 0 -i 0|0 -i 0 0|0 0 0 e^-ip/6 |
41 | Deutsch, D ? | | | | | | | | 3 | |1 0 0 0 0 0 0 0|0 1 0 0 0 0 0 0|0 0 1 0 0 0 0 0|0 0 0 1 0 0 0 0|0 0 0 0 1 0 0 0|0 0 0 0 0 1 0 0|0 0 0 0 0 0 icos? ? sin?|0 0 0 0 0 0 sin? icos? |
42 | Margolus, M, RCCX, Simplified Toffoli |  | | | | | | | 3 | |1 0 0 0 0 0 0 0|0 1 0 0 0 0 0 0|0 0 1 0 0 0 0 0|0 0 0 1 0 0 0 0|0 0 0 0 1 0 0 0|0 0 0 0 0 -1 0 0|0 0 0 0 0 0 0 1|0 0 0 0 0 0 1 0 |
43 | Peres, PG |  | | | | | | | 3 | |1 0 0 0 0 0 0 0|0 1 0 0 0 0 0 0|0 0 1 0 0 0 0 0|0 0 0 1 0 0 0 0|0 0 0 0 0 0 0 1|0 0 0 0 0 0 1 0|0 0 0 0 1 0 0 0|0 0 0 0 0 1 0 0 |
44 | Toffoli, CCNOT, CCX, Toff, Controlled controlled NOT |  | | | | | | | 3 | |1 0 0 0 0 0 0 0|0 1 0 0 0 0 0 0|0 0 1 0 0 0 0 0|0 0 0 1 0 0 0 0|0 0 0 0 1 0 0 0|0 0 0 0 0 1 0 0|0 0 0 0 0 0 0 1|0 0 0 0 0 0 1 0 |