Table of Contents
Quantum gate
Quantum gates are unitary operations that transform quantum states. Like classical logic gates (AND, OR, NOT), quantum gates manipulate qubits – but they preserve superposition and enable entanglement. Every quantum gate is reversible (unitary matrix $U$ satisfies $U^\dagger U = I$).
A quantum gate on $n$ qubits is represented by a $2^n \times 2^n$ unitary matrix. It's an element of Lie group $\mathrm{SU}(2^n)$. Applying a gate to a state $|\psi\rangle$ gives a new state $U|\psi\rangle$. Gates compose: two gates in sequence is a new gate (matrix product).
Single-qubit gates act on one qubit; two-qubit gates entangle or correlate pairs; multi-qubit gates generalize. Any quantum computation can be decomposed into universal gate sets (e.g., single-qubit rotations + CNOT).