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

• URL: http://arxiv.org/abs/2508.14670v1
• Date: Wed, 20 Aug 2025 12:43:42 GMT
• Title: A Complete and Natural Rule Set for Multi-Qutrit Clifford Circuits
• Authors: Sarah Meng Li, Michele Mosca, Neil J. Ross, John van de Wetering, Yuming Zhao,
• Abstract summary: We present a complete set of rewrite rules for n-qutrit Clifford circuits where n is any non-negative integer.<n>This is the first completeness result for any fragment of quantum circuits in odd prime dimensions.
• Score: 1.799352931634487
• License: http://creativecommons.org/licenses/by/4.0/
• 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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