hardware natives 1 qubit 1 parameter
GPi
IonQ's native $\pi$ pulse, a bit flip about the equatorial Bloch-sphere axis at angle $\phi$.
The GPi gate is one of IonQ's native gates: a $\pi$ rotation about an axis in the equatorial plane of the Bloch sphere, at azimuthal angle $\phi$. Physically it is a resonant Rabi pulse whose phase sets $\phi$.
$$ \mathrm{GPi}(\phi) = \begin{bmatrix} 0 & \mathrm{e}^{-i\phi} \\ \mathrm{e}^{i\phi} & 0 \end{bmatrix} $$
Special values
| $\phi$ | Gate |
|---|---|
| $0$ | Pauli-$X$ |
| $\pi/2$ | Pauli-$Y$ |
Properties
- Hermitian and self-inverse for every $\phi$: $\mathrm{GPi}(\phi)^2 = I$.
- Always a bit flip: $\mathrm{GPi}(\phi)|0\rangle = \mathrm{e}^{i\phi}|1\rangle$. The angle $\phi$ only changes the relative phase picked up along the way.
- Equal to the general phased rotation at $\theta = \pi$, up to global phase: $\mathrm{GPi}(\phi) = i \, R(\pi, \phi)$.
Usage
- Together with GPi2 and the Mølmer–Sørensen interaction, this forms IonQ's native gate set; circuits submitted in native-gate mode compile to exactly these operations.
The unitary, drawn
Every entry of the matrix as a disc. The area is the transition probability $|U_{jk}|^2$; the colour and the hand are the phase. Rows are outputs $\langle j|$, columns inputs $|k\rangle$, in the computational basis. Each parameter has a slider; play runs through the family along the path of the Quirk link ($\phi = 2\pi t$).
Phase
Disc area $= |U_{jk}|^2$. Hover an entry for its value, or take the JSON.
SDK support
How to call this gate in each framework. Hover a ⓘ for a note; the support matrix compares every gate at once.
| SDK | Name |
|---|---|
| Qiskit | — ⓘ |
| PennyLane | — ⓘ |
| Cirq | cirq_ionq.GPIGate |
| Q# | — |
| PyQuil | — |
| Braket | braket.circuits.gates.GPi |
| BQSKit | bqskit.ir.gates.U1qPiGate ⓘ |
| Qibo | qibo.gates.GPI |
| pytket | pytket.circuit.OpType.GPI ⓘ |
| Stim | — |
| OpenQASM | — |