QuosCode

QuosPict1

QuosPict2

Names

WikiPicture

WikiPictAlt

Qubits

MatrixString

Qubit in state 0

Qubit in state 1

Qubit in arbitrary state

I
Identity
No-op

1	0
0	1

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

S
sqrt-Z
P
Phase S

1	0
0	i

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

1	0
0	e^iπ/4

V
sqrt-X
sqrt-NOT
SX

1/2

1+i	1−i
1-i	1+i

Rx ?
Rotation about x-axis

cosθ/2	−isinθ/2
−isinθ/2	cosθ/2

Ry ?. Rotation about y-axis

cosθ/2	−sinθ/2
sinθ/2	cosθ/2

Rz ?. Rotation about z-axis

e^−iθ/2	0
0	e^iθ/2

Ph d
Phase d
(e^id)I
Global phase

e^iδ

1	0
0	1

P phi
R phi
u1 phi
Phase shift

1	0
0	e^iφ

U ? ? ?
General single qubit rotation

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

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

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

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

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

Barenco
Barenco a ? ?

1	0	0	0
0	1	0	0
0	0	(e^iα)cosθ	−i(e^i(α−ϕ)sinθ
0	0	−i(e^i(α+ϕ))sinθ	(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)sin(a−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