Common
Clifford gate
Definition of quantum circuits
Clifford gate
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...
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