WnWikiNamesWikiPictWikiPictAltQnQuosName1QuosName2QuosPict1QuosPict2QubitsMatrixString
1I, Identity, No-op1I1|1 0|0 1
2Ph, Phase, (e^id)I, Global phase 2Ph1e^id|1 0|0 1
3X, Pauli X, sx, NOT, Bit flip3X1|0 1|1 0
4Y, Pauli Y, sy4Y1|0 -i|i 0
5Z, Pauli Z, sz, Phase flip5Z1|1 0|0 -1
6S, sqrt-Z, P, Phase S6S1|1 0|0 i
7V, sqrt-X, sqrt-NOT, SX7V11/2|1+i 1-i|1-i 1+i
8H, Hadamard, Walsh-Hadamard8H11/sqrt2|1 1|1 -1
9CX, CNOT, XOR, Controlled NOT, Controlled X, Reversible exclusive OR, Feynman9CX2|1 0 0 0|0 1 0 0|0 0 0 1|0 0 1 0
10CdX, CdashX, XNOR, Controlled NOT, Anticontrolled X, Zero control, Control-on-0-NOT, Reversible exclusive NOR 10CdX2|0 1 0 0|1 0 0 0|0 0 1 0|0 0 0 1
11CZ, CPF, CSign, Cphase, Controlled Z, Controlled sign flip, Controlled phase flip11CZ2|1 0 0 0|0 1 0 0|0 0 1 0|0 0 0 -1
12Double-controlled NOT , DCNOT2|1 0 0 0|0 0 1 0|0 0 0 1|0 1 0 0
13Swap 12SwSw2|1 0 0 0|0 0 1 0|0 1 0 0|0 0 0 1
14iSwap, Imaginary swap 13iSwiSw2|1 0 0 0|0 0 i 0|0 i 0 0|0 0 0 1
15Pphi, P phi, R phi, u1 phi, Phase shift 14Pp1|1 0|0 e^if
16T, Phase gate T, Pi/8 gate, P pi/4, Fourth root of Z15T1|1 0|0 e^ip/4
17Controlled phase, C phase f, CR f16CPp2|1 0 0 0|0 1 0 0|0 0 1 0|0 0 0 e^if
18CS, Cntrolled S, Controlled phase S17CS2|1 0 0 0|0 1 0 0|0 0 1 0|0 0 0 i
19Rx, Rx ?, Rotation about x-axis18Rx1|cos?/2 -isin?/2|-isin?/2 cos?/2
20Ry, Ry ?. Rotation about y-axis 19Ry1|cos?/2 -sin?/2|sin?/2 cos?/2
21Rz, Rz ?. Rotation about z-axis 20Rz1|e^-i?/2 0|0 e^i?/2
22XX 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
23YY 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
24ZZ 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
25XY, 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
26Square root swap2|1 0 0 0|0 (1+i)/2 (1-i)/2 0|0 (1-i)/2 (1+i)/2 0|0 0 0 1
27Square root imaginary swap2|1 0 0 0|0 1/sqrt2 i/sqrt2 0|0 i/sqrt2 1/sqrt2 0|0 0 0 1
28Swap (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
29CSwap, 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
30General single qubit rotation, U ? ? ?1|cos?/2 -(e^-i?)sin?/2 (e^-i?)sin?/2 (e^i(?+?))cos?/2
31Barenco, 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??
32B, Berkeley B2|cosp/8 0 0 isinp/8|0 cos3p/8 isin3p/8 0|0 isinp/8 cosp/8 0|isinp/8 0 0 cosp/8
33CSX, controlled square root NOT, controlled square root X, Controlled V2|1 0 0 0|0 1 0 0|0 0 e^ip/4 e^-ip/4|0 0 e^-ip/4 e^ip/4
34Core entangling, Canonical decomposition, N a b c, Can a b c2|(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)
35Dagwood Bumstead, DB2|1 0 0 0|0 cos3p/8 -isin3p/8 0|0 -isin3p/8 cos3p/8 0|0 0 0 1
36Echoed cross resonance, ECR21/sqrt2|0 0 1 i|0 0 i 1|1 -i 0 0|-i 1 0 0
37Fermionic simulation, UfSim ? ?, fSim ? ?2|1 0 0 0|0 cos? -isin? 0|0 -isin? cos? 0|0 0 0 e^i?
38Givens. G ?, Givens ?2|1 0 0 0|0 cos? -sin? 0|0 sin? cos? 0|0 0 0 1
39Magic. Mu21/sqrt2|1 i 0 0|0 0 i 1|0 0 i -1|1 -i 0 0
40Sycamore, Syc, fSim p/2 p/62|1 0 0 0|0 0 -i 0|0 -i 0 0|0 0 0 e^-ip/6
41Deutsch, 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?
42Margolus, M, RCCX, Simplified Toffoli3|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
43Peres, PG3|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
44Toffoli, CCNOT, CCX, Toff, Controlled controlled NOT3|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