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arXiv · 2508.14670

A Complete and Natural Rule Set for Multi-Qutrit Clifford Circuits

Sarah Meng Li·Michele Mosca·Neil J. Ross·John van de Wetering·Yuming Zhao
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Abstract

We present a complete set of rewrite rules for n-qutrit Clifford circuits where n is any non-negative integer. This is the first completeness result for any fragment of quantum circuits in odd prime dimensions. We first generalize Selinger's normal form for n-qubit Clifford circuits to the qutrit setting. Then, we present a rewrite system by which any Clifford circuit can be reduced to this normal form. We then simplify the rewrite rules in this procedure to a small natural set of rules, giving a clean presentation of the group of qutrit Clifford unitaries in terms of generators and relations.

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Sarah Meng Li, Michele Mosca, Neil J. Ross, John van de Wetering, Yuming Zhao. 2025-08-20. A Complete and Natural Rule Set for Multi-Qutrit Clifford Circuits. https://doi.org/10.4204/eptcs.426.2

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