Pauli group

In physics, quantum information and group theory, the Pauli group is a group formed by tensor products of Pauli matrices, including the identity. The single-qubit Pauli group is a 16-element matrix group, consisting of the 4 Pauli matrices each with 4 possible phase factors. The n-qubit Pauli group is a -element group consisting of tensor products of single-qubit Paulis.

In quantum information theory, Pauli groups are important because they are the basis for stabilizer formalism, a widely-used framework for constructing and describing quantum error correction codes using sets of commuting Pauli operators. Stabilizer codes are formed from commuting subgroups of the Pauli group.

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