QnQuosNamesQuosPict1QuosPict2 WnWikiNamesWikiPict1WikiPict2 QubitsMatrixString
10
21
3I 1I
Identity
No-op
1
1 0
0 1
4T 16T
Phase gate T
Pi/8 gate
P pi/4
Fourth root of Z
1
1 0
0 e^ip/4
5Ph 2Ph
Phase
(e^id)I
Global phase
1e^id
1 0
0 1
6Pp 15Pphi
P phi
R phi
u1 phi
Phase shift
1
1 0
0 e^if
7H 8H
Hadamard
Walsh-Hadamard
11/sqrt2
1 1
1 -1
8X 3X
Pauli X
sx
NOT
Bit flip
1
0 1
1 0
9Y 4Y
Pauli Y
sy
1
0 -i
i 0
10Z 5Z
Pauli Z
sz
Phase flip
1
1 0
0 -1
11Rx 19Rx
Rx ?
Rotation about x-axis
1
cos?/2 -isin?/2
-isin?/2 cos?/2
12Ry 20Ry
Ry ?. Rotation about y-axis
1
cos?/2 -sin?/2
sin?/2 cos?/2
13Rz 21Rz
Rz ?. Rotation about z-axis
1
e^-i?/2 0
0 e^i?/2
14V 7V
sqrt-X
sqrt-NOT
SX
11/2
1+i 1-i
1-i 1+i
15S 6S
sqrt-Z
P
Phase S
1
1 0
0 i
16C Pp 17Controlled phase
C phase f
CR f
2
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 e^if
17C X 9CX
CNOT
XOR
Controlled NOT
Controlled X
Reversible exclusive OR
Feynman
2
1 0 0 0
0 1 0 0
0 0 0 1
0 0 1 0
18C Z 11CZ
CPF
CSign
Cphase
Controlled Z
Controlled sign flip
Controlled phase flip
2
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 -1
19C S 18CS
Cntrolled S
Controlled phase S
2
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 i
20Cd X 10CdX
CdashX
XNOR
Controlled NOT
Anticontrolled X
Zero control
Control-on-0-NOT
Reversible exclusive NOR
2
0 1 0 0
1 0 0 0
0 0 1 0
0 0 0 1
21Sw Sw 13Swap
2
1 0 0 0
0 0 1 0
0 1 0 0
0 0 0 1
22iSw iSw 14iSwap
Imaginary swap
2
1 0 0 0
0 0 i 0
0 i 0 0
0 0 0 1
12Double-controlled NOT
DCNOT
2
1 0 0 0
0 0 1 0
0 0 0 1
0 1 0 0
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 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
27Square root imaginary swap
2
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 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
33CSX
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
34Core 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)
35Dagwood Bumstead
DB
2
1 0 0 0
0 cos3p/8 -isin3p/8 0
0 -isin3p/8 cos3p/8 0
0 0 0 1
36Echoed cross resonance
ECR
21/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. Mu
21/sqrt2
1 i 0 0
0 0 i 1
0 0 i -1
1 -i 0 0
40Sycamore
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
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 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