In physics and mathematics, the Pauli group on 1 qubit is the 16-element matrix group consisting of the 2 × 2 identity matrix and all of the Pauli matrices
together with the products of these matrices with the factors and :
The Pauli group is generated by the Pauli matrices, and like them it is named after Wolfgang Pauli.
The Pauli group on n qubits, , is the group generated by the operators described above applied to each of qubits in the tensor product Hilbert space .
As an abstract group, is the central product of a cyclic group of order 4 and the dihedral group of order 8.