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

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.

In Proceedings QPL 2025, arXiv:2508.13619

References in corpus (4)

• Testing the Hilbert space dimension
• Magic state distillation in all prime dimensions using quantum Reed-Muller codes
• Circuit QED: single-step realization of a multiqubit controlled phase gate with one microwave photonic qubit simultaneously controlling $n-1$ microwave photonic qubits
• Generators and Relations for Real Stabilizer Operators