Clifford Group

The Pauli Matrices provide a basis for the density operators of a single qubit. The Clifford group is defined as the group of unitaries that normalize the Pauli group:

$${\mathbf{C}}_{\mathbf{n}}=\{\mathbf{U}|\mathbf{U}{\mathbf{P}}_{\mathbf{n}}{\mathbf{U}}^{†}={\mathbf{P}}_{\mathbf{n}}\}$$