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

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

2004-08-31

arxiv.org/abs/quant-ph/0408190v2

Phys. Rev. A 71, 042315 (2005)

Physics

Quantum Physics

10 pages, RevTeX

Scientific paper

10.1103/PhysRevA.71.042315

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 the integers modulo 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.

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