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

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  • 31 August 2004
Abstract
We describe generalizations of the Pauli group, the Clifford group and stabilizer states for qudits in a Hilbert space of arbitrary dimensions. We examine a link with modular arithmetic, which yields an efficient way of describing the Pauli group and the Clifford group. We further show how an arbitrary Clifford operation can be efficiently decomposed into one and two-qudit operations. The main result of this paper is a non-trivial extension of the description in modular arithmetic of a qudit stabilizer state with linear and quadratic forms, as already existed for qubits.

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