Phase gate implementation using Qiskit. The example applies $P(\pi/2) = S$ to $\lvert +\rangle$, rotating it to $\lvert i\rangle = \frac{1}{\sqrt{2}}(\lvert 0\rangle + i\lvert 1\rangle)$.
from qiskit import QuantumCircuit from qiskit.quantum_info import Statevector import numpy as np qc = QuantumCircuit(1) qc.h(0) # |0> -> |+> qc.p(np.pi / 2, 0) # P(pi/2) = S: |+> -> |i> print(Statevector(qc)) # Statevector([0.70710678+0.j, 0.+0.70710678j], dims=(2,))