quantum gate directory
GPi2
Symbol
$\mathrm{GPi2}$
Qubits: $1$ Parameters: $1$
Description:
IonQ's native $\pi/2$ pulse, a half rotation about the equatorial Bloch-sphere axis at angle $\phi$.
Alternate notations:
- $\mathrm{GPi2}(\phi)$
- $\mathrm{GPI2}(\phi)$
SDK Support
| SDK | Name |
|---|---|
| Qiskit | — ⓘ |
| PennyLane | — ⓘ |
| Cirq |
cirq_ionq.GPI2Gate
|
| Q# | — |
| PyQuil | — |
| Braket |
braket.circuits.gates.GPi2
|
| BQSKit |
bqskit.ir.gates.U1qPi2Gate
ⓘ
|
| Qibo |
qibo.gates.GPI2
|
| pytket |
pytket.circuit.OpType.GPI2
ⓘ
|
| Stim | — |
| OpenQASM | — |
The GPi2 gate is the half-pulse counterpart of GPi: a $\pi/2$ rotation about the equatorial axis at azimuthal angle $\phi$. It is exactly the general phased rotation at $\theta = \pi/2$: $\mathrm{GPi2}(\phi) = R(\pi/2, \phi)$.
$$ \mathrm{GPi2}(\phi) = \frac{1}{\sqrt{2}} \begin{bmatrix} 1 & -i\mathrm{e}^{-i\phi} \\ -i\mathrm{e}^{i\phi} & 1 \end{bmatrix} $$
Special values
| $\phi$ | Gate |
|---|---|
| $0$ | $R_x(\pi/2)$, i.e. $\sqrt{X}$ up to global phase |
| $\pi/2$ | $R_y(\pi/2)$ |
| $\pi$ | $R_x(-\pi/2)$ |
Properties
- Creates equal superpositions: $\mathrm{GPi2}(\phi)$ maps the poles of the Bloch sphere to the equator, making it the hardware-native stand-in for the Hadamard.
- Inverse: $\mathrm{GPi2}(\phi)^\dagger = \mathrm{GPi2}(\phi + \pi)$.
Usage
- On IonQ hardware, arbitrary single-qubit gates are compiled into at most two GPi2 pulses (plus phase bookkeeping): $z$ rotations are virtual — implemented by advancing the phase of all subsequent pulses — so only the equatorial pulses cost real gate time.
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