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