Parity computation by CNOT gates ($W|x⟩|y⟩=|x⟩|y\oplus {⨁}_j{x}_j⟩$)

Apply one CNOT gate from each input qubit to the same target. Their actions commute because controls remain unchanged and each contribution is added modulo two. This reversible circuit computes the parity bit with exactly one two-qubit gate per input, and its inverse is the same circuit. Unlike measuring the inputs to compute parity classically, the unitary preserves quantum superposition and can be uncomputed after phase application.