Stabilizer states and Clifford operations for systems of arbitrary dimensions and modular arithmetic

We describe generalizations of the Pauli group, the Clifford group, and stabilizer states for qudits in a Hilbert space of arbitrary dimension $d$. We examine a link with modular arithmetic, which yields an efficient way of representing the Pauli group and the Clifford group with matrices over ${\mathbb{Z}}_d$. We further show how a Clifford operation can be efficiently decomposed into one and two-qudit operations. We also focus in detail on standard basis expansions of stabilizer states.