quantum-gate
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| + | # Quantum Gate | ||
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| + | **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 $U^\dagger U = I$). | ||
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| + | A quantum gate on $n$ qubits is represented by a $2^n \times 2^n$ unitary matrix. 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). | ||
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| + | 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). | ||
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| + | ## Concepts | ||
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| + | 1. [[quantum-gate-matrices|Gate matrices and notation]] | ||
| + | 2. [[quantum-gate-composition|Gate composition]] | ||
| + | 3. [[quantum-gate-decomposition|Gate decomposition]] | ||
| + | 4. [[quantum-gate-universal|Universal gate sets]] | ||
| + | 5. [[quantum-gate-parametric|Parametric gates]] | ||
| + | 6. [[quantum-gate-clifford|Clifford vs non-Clifford gates]] | ||
| + | 7. [[quantum-gate-physical-implementation|Physical implementation]] | ||
| + | 8. [[quantum-gate-fidelity|Gate fidelity and errors]] | ||
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| + | ## Gates | ||
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| + | - [[quantum-gate-single-qubit]] | ||
| + | - [[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]] | ||
| + | - [[quantum-gate-t|T gate]] | ||
| + | - [[quantum-gate-rx|RX (rotation around X)]] | ||
| + | - [[quantum-gate-ry|RY (rotation around Y)]] | ||
| + | - [[quantum-gate-rz|RZ (rotation around Z)]] | ||
| + | - [[quantum-gate-u|Universal single-qubit (U)]] | ||
| + | - [[quantum-gate-two-qubit]] | ||
| + | - [[quantum-gate-cnot|CNOT (CX)]] | ||
| + | - [[quantum-gate-cz|CZ (Controlled-Z)]] | ||
| + | - [[quantum-gate-swap|SWAP]] | ||
| + | - [[quantum-gate-iswap|iSWAP]] | ||
| + | - [[quantum-gate-cphase|Controlled-Phase]] | ||
| + | - [[quantum-gate-xx|XX (parametric)]] | ||
| + | - [[quantum-gate-yy|YY (parametric)]] | ||
| + | - [[quantum-gate-zz|ZZ (parametric)]] | ||
| + | - [[quantum-gate-three-qubit]] | ||
| + | - [[quantum-gate-toffoli|Toffoli (CCX)]] | ||
| + | - [[quantum-gate-fredkin|Fredkin (CSWAP)]] | ||
| + | - [[quantum-gate-multiqubit|Multi-qubit gates (n-qubit general)]] | ||
| + | - [[quantum-gate-permutation|Permutation gates]] | ||
| + | - [[quantum-gate-grover-diffusion|Grover diffusion operator]] | ||
| + | - [[quantum-gate-qft|Quantum Fourier Transform]] | ||
| + | - [[quantum-gate-phase-oracle|Phase oracle gates]] | ||