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quantum algorithms:
The Pauli group is the finite group of order 16 which is isomorphic to the subgroup of the complex general linear group that consists of the multiples by and (where “” denotes the imaginary unit) of the four Pauli matrices :
where
In quantum information theory one often considers the “higher” or “-qbit” Pauli groups whose elements are (multiples by , ) of -fold tensor products of the Pauli matrices.
The normalizer subgroup of the -qbit Pauli group inside the unitary group is known as the corresponding Clifford group.
The quaternion group is the (normal) subgroup of the Pauli group (1) omitting the -phases on nonidentity matrices:
In fact, the Pauli group is a semidirect product group of the quaternion group with the cyclic group of order 2:
In the comtext of quantum computing:
See also:
Discussion in the context of quantum error correction codes:
Last revised on April 8, 2025 at 12:02:42. See the history of this page for a list of all contributions to it.