We recall the definition of a Clifford group (over $n$ qubits) is the set of unitary transformations:

$$\{U: UPU^\dagger\in\mathcal{P}\}$$

where $\mathcal{P}$ denotes the corresponding Pauli group (again over $n$ qubits).

What progress has been made in characterizing the subgroups of the Clifford group, and in particular, what progress has been made in characterizing those subgroups isomorphic to the Pauli Group?

This post imported from StackExchange Physics at 2014-06-19 11:26 (UCT), posted by SE-user ruadath