circuit-level n qubits 1 parameter
Global Phase
Multiplies the entire quantum state by an overall phase factor.
A global phase gate applies $e^{i\phi}$ to the entire state. It has no observable effect on measurement probabilities or expectation values. On a single qubit:
$$ \mathrm{Ph}(\phi) = \mathrm{e}^{i\phi} I = \begin{bmatrix} \mathrm{e}^{i\phi} & 0 \\ 0 & \mathrm{e}^{i\phi} \end{bmatrix} $$
Properties
- Physically unobservable on a closed system; only relative phases matter.
- Commutes with all gates.
Usage
- Often ignored in circuit optimization and compilation.
- Appears when simplifying products of rotations.
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, shown for $n = 1$. Each parameter has a slider; play runs through the family along the path of the Quirk link ($\phi = \pi/2$).
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 | qiskit.circuit.library.GlobalPhaseGate |
| PennyLane | pennylane.GlobalPhase ⓘ |
| Cirq | cirq.GlobalPhaseGate |
| Q# | — ⓘ |
| PyQuil | — ⓘ |
| Braket | braket.circuits.gates.GPhase ⓘ |
| BQSKit | — |
| Qibo | — ⓘ |
| pytket | pytket.circuit.OpType.Phase ⓘ |
| Stim | — |
| OpenQASM | gphase |