quantum gate directory
Global Phase
Symbol
$\mathrm{Ph}$
Description:
Multiplies the entire quantum state by an overall phase factor.
Alternate notations:
- $\mathrm{e}^{i\phi}$
- $\mathrm{e}^{i\phi} I$
SDK Support
| SDK | Name |
|---|---|
| Qiskit |
qiskit.circuit.library.GlobalPhaseGate
|
| PennyLane |
pennylane.GlobalPhase
|
| Cirq |
cirq.GlobalPhaseGate
|
| Q# | — |
| PyQuil | — |
| Braket | — |
| BQSKit | — |
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.
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