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

2025/08/20 by Li, Sarah Meng, Mosca, Michele, Ross, Neil J. +2 · 3 citations
#FOS: Computer and information sciences #FOS: Physical sciences #Logic in Computer Science (cs.LO) #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.2508.14670

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.

Citations

• Qudit Noisy Stabilizer Formalism
• Synthesis of Single Qutrit Circuits from Clifford+R
• Qudit-based quantum error-correcting codes from irreducible representations of SU(d)
• Scalable improvement of the generalized Toffoli gate realization using trapped-ion-based qutrits
• Low Overhead Qutrit Magic State Distillation
• Completeness of the ZH-calculus
• Diagrammatic Reasoning beyond Clifford+T Quantum Mechanics
• A universal completion of the ZX-calculus

Cited by

• Simpler Presentations for Many Fragments of Quantum Circuits
• GCAMPS: A Scalable Classical Simulator for Qudit Systems
• Transversal AND in Quantum Codes

Related

• Simpler Presentations for Many Fragments of Quantum Circuits
• A Normal Form for Single-Qudit Clifford+T Operators
• Synthesis of Single Qutrit Circuits from Clifford+R
• Synthesis of unitaries with Clifford+T circuits
• The exact synthesis of 1- and 2-qubit Clifford+T circuits