QuosCode

QuosPict1

QuosPict2

Names

WikiPicture

WikiPictAlt

Qubits

MatrixString

Qubit in state 0

Qubit in state 1

I
Identity
No-op

1 0

0 1

T
Phase gate T
Pi/8 gate
P pi/4
Fourth root of Z

1 0

0 e^iπ/4

Ph
Phase
(e^id)I
Global phase

e^iδ

1 0

0 1

Pphi
P phi
R phi
u1 phi
Phase shift

1 0

0 e^iφ

H
Hadamard
Walsh-Hadamard

1/√2

1 1

1 -1

X
Pauli X
sx
NOT
Bit flip

0 1

1 0

Y
Pauli Y
sy

0 −i

i 0

Z
Pauli Z
sz
Phase flip

1 0

0 −1

Rx
Rx ?
Rotation about x-axis

cosθ/2 −isinθ/2

−isinθ/2 cosθ/2

Ry
Ry ?. Rotation about y-axis

cosθ/2 −sinθ/2

sinθ/2 cosθ/2

Rz
Rz ?. Rotation about z-axis

e^−iθ/2 0

0 e^iθ/2

V
sqrt-X
sqrt-NOT
SX

1/2

1+i 1−i

1-i 1+i

S
sqrt-Z
P
Phase S

1 0

0 i

C Pp

Controlled phase
C phase f
CR f

1 0 0 0

0 1 0 0

0 0 1 0

0 0 0 e^iφ

C X

CX
CNOT
XOR
Controlled NOT
Controlled X
Reversible exclusive OR
Feynman

1 0 0 0

0 1 0 0

0 0 0 1

0 0 1 0

C Z

CZ
CPF
CSign
Cphase
Controlled Z
Controlled sign flip
Controlled phase flip

1 0 0 0

0 1 0 0

0 0 1 0

0 0 0 -1

C S

CS
Cntrolled S
Controlled phase S

1 0 0 0

0 1 0 0

0 0 1 0

0 0 0 i

Cd X

CdX
CdashX
XNOR
Controlled NOT
Anticontrolled X
Zero control
Control-on-0-NOT
Reversible exclusive NOR

0 1 0 0

1 0 0 0

0 0 1 0

0 0 0 1

Sw Sw

Swap

1 0 0 0

0 0 1 0

0 1 0 0

0 0 0 1

iSw iSw

iSwap
Imaginary swap

1 0 0 0

0 0 i 0

0 i 0 0

0 0 0 1

Measurement gate

Observation gate

Komparator
Comparator

Double-controlled NOT
DCNOT

1 0 0 0

0 0 1 0

0 0 0 1

0 1 0 0

XX interaction
Rxx ?
XX ?

cosϕ/2 0 0 −isinϕ/2

0 cosϕ/2 −isinϕ/2 0

0 −isinϕ/2 cosϕ/2 0

−isinϕ/2 0 0 cosϕ/2

YY interaction
Ryy ?
YY ?

cosϕ/2 0 0 isinϕ/2

0 cosϕ/2 −isinϕ/2 0

0 −isinϕ/2 cosϕ/2 0

isinϕ/2 0 0 cosϕ/2

ZZ interaction
Rzz ?
ZZ ?

e^−iϕ/2 0 0 0

0 e^−iϕ/2 0 0

0 0 e^−iϕ/2 0

0 0 0 e^−iϕ/2

XY
XX plus YY
Rxy ?
XY ?

1 0 0 0

0 cosϕ/2 −isinϕ/2 0

0 −isinϕ/2 cosϕ/2 0

0 0 0 1

Square root swap

1 0 0 0

0 (1+i)/2 (1−i)/2 0

0 (1−i)/2 (1+i)/2 0

0 0 0 1

Square root imaginary swap

1 0 0 0

0 1/sqrt2 i/sqrt2 0

0 i/sqrt2 1/sqrt2 0

0 0 0 1

Swap (raised to a power)

1 0 0 0

0 (1+e^iπα)/2 (1−e^iπα)/2 0

0 (1−e^iπα)/2 (1+e^iπα)/2 0

0 0 0 1

CSwap
Controlled swap
Fredkin

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

General single qubit rotation
U ? ? ?

cosθ/2 -(e^−iλ)sinθ/2 (e^−iϕ)sinθ/2 (e^i(λ+ϕ))cosθ/2

Barenco
Barenco a ? ?

1 0 0 0

0 1 0 0

0 0 (e^iα)cos⁡ θ −i(e^i(α−ϕ)sinθ

0 0 −i(e^i(α+ϕ))sin⁡ θ (e^iα)cos⁡θ

B
Berkeley B

cosπ/8 0 0 isinπ/8

0 cos3π/8 isin3π/8 0

0 isinπ/8 cosπ/8 0

isinπ/8 0 0 cosπ/8

CSX
controlled square root NOT
controlled square root X
Controlled V

1 0 0 0

0 1 0 0

0 0 e^iπ/4 e^−iπ/4

0 0 e^−iπ/4 e^iπ/4

Core entangling
Canonical decomposition
N a b c
Can a b c

(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)

Dagwood Bumstead
DB

1 0 0 0

0 cos3π/8 −isin3π/8 0

0 −isin3π/8 cos3π/8 0

0 0 0 1

Echoed cross resonance
ECR

1/sqrt2

0 0 1 i

0 0 i 1

1 −i 0 0

−i 1 0 0

Fermionic simulation
UfSim ? ?
fSim ? ?

1 0 0 0

0 cosθ −isinθ 0

0 −isinθ cosθ 0

0 0 0 e^iϕ

Givens. G ?
Givens ?

1 0 0 0

0 cosθ −sinθ 0

0 sinθ cosθ 0

0 0 0 1

Magic. Mu

1/sqrt2

1 i 0 0

0 0 i 1

0 0 i −1

1 −i 0 0

Sycamore
Syc
fSim p/2 p/6

1 0 0 0

0 0 −i 0

0 −i 0 0

0 0 0 e^−iπ/6

Deutsch
D ?

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⁡ θ sinθ
0 0 0 0 0 0 sinθ icosθ

Margolus
M
RCCX
Simplified Toffoli

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

Peres
PG

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

Toffoli
CCNOT
CCX
Toff
Controlled controlled NOT

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