Pauli group

In physics and mathematics, the Pauli group $G_1$ on 1 qubit is the matrix group consisting of the identity matrix $I$ and all of the Pauli matrices $X=\sigma_1$ , $Y=\sigma_2$ , $Z=\sigma_3$ , together with multiplicative factors $\pm1,\pm i$ :

$G_1 \ \stackrel{\mathrm{def}}{=}\ \{\pm I,\pm iI,\pm X,\pm iX,\pm Y,\pm iY,\pm Z,\pm iZ\} \equiv \langle X, Y, Z \rangle$ .

The Pauli group is generated by the Pauli matrices.

The Pauli group on n qubits, $G_n$ , is the group generated by the operators described above applied to each of $n$ qubits in the tensor product Hilbert space $(\mathbb{C}^2)^{\otimes n}$ .

References

Nielsen, Michael A; Chuang, Isaac L (2000). Quantum Computation and Quantum Information. Cambridge; New York: Cambridge University Press. ISBN 9780521632355. OCLC 43641333.