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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).
Concepts
Gates
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- Clifford gates
- [[quantum-gate-pauli]] - [[quantum-gate-i|Identity (I)]] - [[quantum-gate-x|Pauli X (NOT)]] - [[quantum-gate-y|Pauli Y]] - [[quantum-gate-z|Pauli Z]] - [[quantum-gate-h|Hadamard (H)]] - [[quantum-gate-s|S (Phase) gate]]
- T gate
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