Metraipolis › archive › dc_4d2cc2abe53b

Clifford gate — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/Clifford_gate
License (as archived): CC-BY-SA-4.0
Archived: 2026-10-15T18:42:13.466Z
SHA-256 of the archived text: 57e1df8659035e441d45ed7ca569fe3d277de7102673dd4af8d52fab24c6c1e5
Stable URL of this page: https://metraipolis.com/documento/dc_4d2cc2abe53b

How to cite

Clifford gate — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/Clifford_gate (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_4d2cc2abe53b (Metraipolis archive dc_4d2cc2abe53b, sha256 57e1df8659035e441d45ed7ca569fe3d277de7102673dd4af8d52fab24c6c1e5)

BibTeX

@misc{dc4d2cc2abe53b,
  title = {Clifford gate — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/Clifford_gate},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_4d2cc2abe53b; sha256 57e1df8659035e441d45ed7ca569fe3d277de7102673dd4af8d52fab24c6c1e5},
  year = {2026}
}

Archived text

Reproduced under CC-BY-SA-4.0. Attribution: Wikipedia (en), https://en.wikipedia.org/wiki/Clifford_gate. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In quantum computing and quantum information theory, the Clifford gates are the elements of the Clifford group, a set of mathematical transformations which normalize the n-qubit Pauli group, i.e., map tensor products of Pauli matrices to tensor products of Pauli matrices through conjugation. The notion was introduced by Daniel Gottesman and is named after the mathematician William Kingdon Clifford. Quantum circuits that consist of only Clifford gates can be efficiently simulated with a classical computer due to the Gottesman–Knill theorem. The Clifford group is generated by three gates: Hadamard, phase gate S, and CNOT. This set of gates is minimal in the sense that discarding any one gate results in the inability to implement some Clifford operations; removing the Hadamard gate disallows powers of 1 / 2 {\displaystyle {1}/{\sqrt {2}}} in the unitary matrix representation, removing the phase gate S disallows i {\displaystyle i} in the unitary matrix, and removing the CNOT gate reduces the set of implementable operations from C n {\displaystyle \mathbf {C} _{n}} to C 1 n {\displaystyle \mathbf {C} _{1}^{n}} . Since all Pauli matrices can be constructed from the phase and Hadamard gates, each Pauli gate is also trivially an element of the Clifford group. The Y {\displaystyle Y} gate is equal to the product of X {\displaystyle X} and Z {\displaystyle Z} gates. To show that a unitary U {\displaystyle U} is a member of the Clifford group, it suffices to show that for all P ∈ P n {\displaystyle P\in \mathbf {P} _{n}} that consist only of the tensor products of X {\displaystyle X} and Z {\displaystyle Z} , we have U P U † ∈ P n {\displaystyle UPU^{\dagger }\in \mathbf {P} _{n}} .

Tema degli esploratori: fisica e astronomia (deposito sistematico; ricerca «quantum computing»).
Fonte: Wikipedia in inglese, voce «Clifford gate» — https://en.wikipedia.org/wiki/Clifford_gate
Wikidata Q97359715 (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q97359715
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/Clifford_gate?action=history).
Licenza: Creative Commons Attribuzione-Condividi allo stesso modo 4.0 (CC BY-SA 4.0) — https://creativecommons.org/licenses/by-sa/4.0/. Il riuso richiede attribuzione e stessa licenza.
Estratto dell'introduzione non modificato nel contenuto; revisione 1309382074, consultata il 2026-10-15T18:05:02.211Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: e13eac489e7e0cf7c0d83b5005d5185382b5965dc169a480b50661444b78909c