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--- quantum-gate [May 25, 2026 at 10:14] – Ivan Janevski
+++ quantum-gate [August 22, 2026 at 22:15] (current) – external edit 127.0.0.1
@@ Line 1: / Line 1: @@
-# Quantum gate
+# Quantum Gate
-**Quantum gates** are the quantum computing equivalent of classical logic gates like AND, OR, XOR, NOT.
-Classical logic gates are defined by their truth tables. They follow a mathematical structure called Boolean algebra. With the advancement of MOSFET transistor it became possible to implement these logic gates electrically.
+**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 $U^\dagger U = I$).
-Quantum gates work in a similar way. They are defined by matrices. They follow the rules of a mathematical structure called the Lie group.
+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).
+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).
-## List of quantum gates
+## Concepts
+. [[quantum-gate-matrices|Gate matrices and notation]]
+. [[quantum-gate-composition|Gate composition]]
+. [[quantum-gate-decomposition|Gate decomposition]]
+. [[quantum-gate-universal|Universal gate sets]]
+. [[quantum-gate-parametric|Parametric gates]]
+. [[quantum-gate-clifford|Clifford vs non-Clifford gates]]
+. [[quantum-gate-physical-implementation|Physical implementation]]
+. [[quantum-gate-fidelity|Gate fidelity and errors]]
+## Gates
+- [[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]]
- - [[i-gate]]
- - [[x-gate]]
- - [[y-gate]]
- - [[z-gate]]
- - [[r-gate]]
- - [[s-gate]]
- - [[t-gate]]
- - [[h-gate]]
- - [[p-gate]]
- - [[u-gate]]
- - [[ccnot-gate]]
- - [[cnot-gate]]
- - [[swap-gate]]
- - [[iswap-gate]]