quantum gate directory

Quantum gates are the fundamental building block of quantum computation. This website aims to provide information regarding quantum gates seen in literature, and in practice in building quantum computers.


Periodic Table of Gates

Each cell shows the gate symbol with its arity and quDit dimension in the top right (e.g. 2q2d for a two-qubit gate).

Highlight: Hover or click a filter to emphasize matching gates.
2q2d
$B$
B Gate
 2q2d
$\mathrm{CAN}$
Canonical entangling
 2q2d
$\mathrm{C}X$
Controlled Not
 2q2d
$\mathrm{C}P(\phi)$
Controlled Phase
 3q2d
$\mathrm{CSWAP}$
Fredkin
 2q2d
$\mathrm{C}\sqrt{X}$
Controlled sqrt(X)
 2q2d
$\mathrm{C}Z$
Controlled-Z
 2q2d
$\mathrm{DC}X$
Double CX
 2q2d
$ECR$
Echoed Cross-Resonance
 2q2d
$\mathrm{fSWAP}$
fSWAP
 2q2d
$G(\theta)$
Givens Rotation
 nq2d
$\mathrm{Ph}(\phi)$
Global Phase
 1q2d
$H$
Hadamard
 nq2d
$I$
Identity
 2q2d
$i\mathrm{SWAP}$
iSWAP
 2q2d
$M$
Magic
 nq2d
$MS$
Mølmer-Sørensen
 nqpd
$O_f$
Oracle
 1q2d
$X$
Pauli-X
 1q2d
$Y$
Pauli-Y
 1q2d
$Z$
Pauli-Z
 nqpd
$O_f^\pm$
Phase Oracle
 1q2d
$P(\phi)$
Phase Shift
 nq2d
$\mathrm{QFT}_n$
Quantum Fourier Transform
 1q2d
$R_{\mathbf{n}}(\theta)$
Arbitrary Rotation
 1q2d
$R_x$
$x$ Rotation
 2q2d
$R_{xx}$
$xx$ Rotation
 1q2d
$R_y$
$y$ Rotation
 2q2d
$R_{yy}$
$yy$ Rotation
 1q2d
$R_z$
$z$ Rotation
 2q2d
$R_{zz}$
$zz$ Rotation
 1q2d
$S$
Phase
 2q2d
$\sqrt{\mathrm{SWAP}}$
Square Root SWAP
 2q2d
$\mathrm{SWAP}$
SWAP
 1q2d
$\sqrt{X}$
Square Root of X
 1q2d
$T$
T
 1q2d
$G$
unnamed
 3q2d
$\mathrm{CC}X$
Toffoli
 1q2d
$U_3$
U3
 2q2d
$B^{(2)}_i$
Virtual Distillation

Groups

Subgroups of the unitary group $\mathsf{U}(n)$ that are of particular importance.


Not finding a gate you're interested in? Open an issue and we'll add it!