Quantum Circuits

Composing Gates

A quantum circuit is a sequence of gates applied to qubits. Gates are applied left to right (first gate first).

We can represent a circuit as a list of gate functions and apply them in order:

def apply_gates(state, gates):
    for gate in gates:
        state = gate(state)
    return state

Example: $H o X o H = Z$

Applying these three gates in sequence to $|0 angle$ is equivalent to applying the Z gate:

import math

def hadamard(state):
    s = 1 / math.sqrt(2)
    a, b = state[0], state[1]
    return [s * (a + b), s * (a - b)]

def x_gate(state):
    return [state[1], state[0]]

zero = [1.0, 0.0]
result = apply_gates(zero, [hadamard, x_gate, hadamard])
print(round(result[0], 4))  # 1.0 — same as Z|0⟩ = |0⟩
print(round(result[1], 4))  # 0.0

This is called a circuit identity: $H cdot X cdot H = Z$.

Your Task

Implement apply_gates(state, gates) and verify three circuit identities.