Computing Library › Quantum Logic Gates
Quantum Logic Gates
Phase Gate P(φ)
The general phase gate P(φ) adds an arbitrary phase φ to |1⟩ — the parametric family that contains S (φ=π/2) and T (φ=π/4).
Matrix
Unitary matrix
100e^{iφ}
Circuit symbol
Action on basis states
| input | output |
|---|---|
| |0⟩ | |0⟩ |
| |1⟩ | e^{iφ}|1⟩ |
How it works
P(φ) equals Rz(φ) up to a global phase. It is the diagonal building block of the quantum Fourier transform, where controlled-P gates apply the fractional phases that encode the transform.
In code (Qiskit)
python
qc = QuantumCircuit(1)
qc.p(0.3, 0)single-qubitparametricphase