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--- quantum-gate [June 12, 2026 at 22:00] – external edit 127.0.0.1
+++ quantum-gate [June 13, 2026 at 03:13] (current) – external edit 127.0.0.1
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 Classical logic gates like AND and OR are irreversible — given only the output, you cannot recover both inputs. Quantum gates cannot be irreversible in this way because unitary evolution is bijective. The only irreversible step in a quantum computation is **measurement**, which collapses the state vector and cannot be undone.
-Single-qubit gates are $2 \times 2$ unitary matrices. The most general single-qubit gate is the [[u-gate|U gate]] $U(\theta, \phi, \lambda)$, which subsumes all others as special cases. Two-qubit gates are $4 \times 4$ unitary matrices; the [[cnot-gate|CNOT gate]] is the standard entangling two-qubit gate. Together, single-qubit gates and CNOT form a universal gate set: any $n$-qubit unitary can be approximated to arbitrary precision using only these.
+Single-qubit gates are $2 \times 2$ unitary matrices. The most general single-qubit gate is the [[u-gate|U gate]] $U(\theta, \phi, \lambda)$, which subsumes all others as special cases. Two-qubit gates are $4 \times 4$ unitary matrices; the [[cx-gate|CX gate]] is the standard entangling two-qubit gate. Together, single-qubit gates and CX form a universal gate set: any $n$-qubit unitary can be approximated to arbitrary precision using only these.
-## List of quantum gates
- - [[pauli-gates]] — the four Pauli matrices $I, X, Y, Z$ as a group
- - [[i-gate]] — identity
- - [[x-gate]] — bit flip (Pauli-X)
- - [[y-gate]] — bit and phase flip (Pauli-Y)
- - [[z-gate]] — phase flip (Pauli-Z)
- - [[h-gate]] — Hadamard
- - [[rotation-gates]] — rotation gates $R_x, R_y, R_z$
- - [[p-gate]] — phase gate (generalizes $Z$, $S$, $T$)
- - [[u-gate]] — universal single-qubit gate
- - [[multiqubit-gates]] — overview of two- and three-qubit gates
- - [[cnot-gate]] — controlled-NOT
- - [[toffoli-gate]] — doubly-controlled-NOT (CCNOT)
- - [[swap-gate]] — qubit swap
- - [[iswap-gate]] — swap with imaginary phase