quantum gate directory

Paulis & basics

1 $X$ Pauli-X 1 $Y$ Pauli-Y 1 $Z$ Pauli-Z

n $I$ Identity 1 $H$ Hadamard

roots

1 $\sqrt{X}$ Square Root of X $\sqrt{Y}$ unclaimed 1 $S$ Phase 1 $T$ T

1 $G$ unnamed 1 2 $U_2$ U2

rotations

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

rotationscontrolled

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

controlled

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)

controlledmulti-qubit

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

swap family

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

hardware natives

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

interactions

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

qudits

1 $X_d$ Shift 1 $Z_d$ Clock 1 $C_d$ Chrestenson 2 $\mathrm{SUM}_d$ Controlled Shift (SUM) 2 $\mathrm{C}Z_d$ Controlled Clock

circuit-level

n 1 $\mathrm{Ph}$ Global Phase n $\mathrm{QFT}_n$ Quantum Fourier Transform n $O_f$ Oracle n $O_f^\pm$ Phase Oracle n $U_s$ Grover Diffuser

2 $B^{(2)}_i$ Virtual Distillation