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

Erik Hostens·Jeroen Dehaene·Bart De Moor
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Abstract

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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Erik Hostens, Jeroen Dehaene, Bart De Moor. 2005-02-22. Stabilizer states and Clifford operations for systems of arbitrary dimensions, and modular arithmetic. https://doi.org/10.1103/physreva.71.042315

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