Published by the American Physical Society through the American Institute of Physics
Physical Review A, Atomic, Molecular and Optical Physics vol:71 issue:4 pages:043215
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 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.