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Clifford circuits over non-cyclic abelian groups
M. Moses, Jacek Horecki, Konrad Deka, Jan Tułowiecki·February 21, 2024
Physics
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Abstract
We present a discussion of the generalized Clifford group over non-cyclic finite abelian groups. These Clifford groups appear naturally in the theory of topological error correction and abelian anyon models. We demonstrate a generalized Gottesman-Knill theorem, stating that every Clifford circuit can be efficiently classically simulated. We additionally provide circuits for a universal quantum computing scheme based on local two-qudit Clifford gates and magic states.