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 · Electronic Proceedings in Theoretical Computer Science · 2025
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.