Abstract:
In this Lecture we study algebraic properties of the Pauli group and stabilizer subgroups for the case of multiqubit systems. The Pauli group is quite simple to describe: we can think of it as “abelian” modulo phases. Any two Pauli operators either commute or anticommute; non-identity Pauli operators have zero trace. A stabilizer subgroup in a Pauli group is an abelian subgroup consisting of self-adjoint operators and not containing $-I$. Stabilizer subgroups have a set of generators, the choice of which determines the stabilizer tableau. Maximal stabilizer groups correspond to an important class of stabilizer states.
