Editing Quantum logic gate (section)

{{short description|Basic circuit in quantum computing}}
{{redirect-distinguish|Quantum gate|Quantum Gate (video game)|Quantum Gate (album)}}
[[File:Quantum Logic Gates.png|thumb|right|upright=2 |Common quantum logic gates by name (including abbreviation), circuit form(s) and the corresponding unitary matrices]]
{{Use American English|date=April 2019}}
In [[quantum computing]] and specifically the [[quantum circuit]] [[model of computation]], a '''quantum logic gate''' (or simply '''quantum gate''') is a basic quantum circuit operating on a small number of [[qubit]]s. Quantum logic gates are the building blocks of quantum circuits, like classical [[logic gate]]s are for conventional digital circuits.

Unlike many classical logic gates, quantum logic gates are [[reversible computing|reversible]]. It is possible to perform classical computing using only reversible gates. For example, the reversible [[Toffoli gate]] can implement all [[Boolean function]]s, often at the cost of having to use [[ancilla bit]]s. The Toffoli gate has a direct quantum equivalent, showing that quantum circuits can perform all operations performed by classical circuits.

Quantum gates are [[unitary operators]], and are described as [[unitary matrix|unitary matrices]] relative to some [[orthonormal]] [[Basis (linear algebra)|basis]]. Usually the ''computational basis'' is used, which unless comparing it with something, just means that for a ''d''-level quantum system (such as a [[qubit]], a [[quantum register]], or [[qutrit]]s and [[qudit]]s){{r|Williams|pages=22–23}} the [[orthonormal basis]] [[Vector space|vector]]s are labeled {{nowrap|<math>|0\rangle, |1\rangle, \dots, |d-1\rangle</math>,}} or use [[Binary number|binary notation]].