quantum gate directory

1

$X$

Pauli-X

1

$Y$

Pauli-Y

1

$Z$

Pauli-Z

n

$I$

Identity

1

$H$

Hadamard

1

$\sqrt{X}$

Square Root of X

$\sqrt{Y}$

unclaimed

1

$S$

Phase

1

$T$

T

1

$G$

unnamed

1 2

$U_2$

U2

1 1

$R_x$

x Rotation

1 1

$R_y$

y Rotation

1 1

$R_z$

z Rotation

1 1

$P$

Phase Shift

1 2

$R(\theta, \phi)$

Phased Rotation

1 3

$R_{\mathbf{n}}$

Arbitrary Rotation

1 3

$U_3$

U3

2 1

$R_{xx}$

xx Rotation

2 1

$R_{yy}$

yy Rotation

2 1

$R_{zz}$

zz Rotation

2 1

$R_{zx}$

zx Rotation

2 1

$\mathrm{C}R_x$

Controlled x Rotation

2 1

$\mathrm{C}R_y$

Controlled y Rotation

2 1

$\mathrm{C}R_z$

Controlled z Rotation

2

$\mathrm{C}X$

Controlled Not

2

$\mathrm{C}Y$

Controlled-Y

2

$\mathrm{C}Z$

Controlled-Z

2 1

$\mathrm{C}P$

Controlled Phase

2

$\mathrm{C}H$

Controlled-Hadamard

2

$\mathrm{C}S$

Controlled-S

2

$\mathrm{C}\sqrt{X}$

Controlled sqrt(X)

3

$\mathrm{CC}X$

Toffoli

3

$\mathrm{CC}Z$

Controlled-CZ

3

$\mathrm{CSWAP}$

Fredkin

n+1

$\mathrm{C}^nX$

Multi-Controlled X

3 1

$D(\theta)$

Deutsch

3

$\mathrm{RCC}X$

Margolus

2

$\mathrm{SWAP}$

SWAP

2

$i\mathrm{SWAP}$

iSWAP

2

$\sqrt{\mathrm{SWAP}}$

Square Root SWAP

2

$\sqrt{i\mathrm{SWAP}}$

Square Root iSWAP

2

$\mathrm{fSWAP}$

fSWAP

2

$\mathrm{DC}X$

Double CX

1 1

$\mathrm{GPi}$

GPi

1 1

$\mathrm{GPi2}$

GPi2

n n(n-1)/2

$MS$

Mølmer-Sørensen

2

$ECR$

Echoed Cross-Resonance

2

$\mathrm{SYC}$

Sycamore

2 1

$\mathrm{XY}$

XY Interaction

2 2

$\mathrm{FSim}$

Fermionic Simulator

2 3

$\mathrm{CAN}$

Canonical entangling

2

$B$

B Gate

2

$M$

Magic

2 1

$G_{ij}$

Givens Rotation

2 1

$R_{xx-yy}$

XX−YY Interaction