A Complete and Natural Rule Set for Multi-Qutrit Clifford Circuits
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.
Authors
- Neil J. Ross (ORCID: https://orcid.org/0000-0003-0941-4333)
- Michele Mosca (ORCID: https://orcid.org/0000-0001-7076-3095)
- John van de Wetering (ORCID: https://orcid.org/0000-0002-5405-8959)
- Sarah Meng Li (ORCID: https://orcid.org/0000-0002-1415-4145)
- Yuming Zhao (ORCID: https://orcid.org/0000-0003-1748-6441)
Institutions
- Dalhousie University (CA)
- University of Waterloo (CA)
- University of Amsterdam (NL)
Publication Details
- Journal
- Electronic Proceedings in Theoretical Computer Science
- Published
- 2025-08-19
- DOI
- https://doi.org/10.4204/eptcs.426.2
- Citations
- 1
- Primary Topic
- Quantum-Dot Cellular Automata
- Type
- article
- Field-Weighted Citation Impact
- 1.50
Funders
- Villum Fonden
- Innovation, Science and Economic Development Canada
- Government of Canada
- Institut Périmètre de physique théorique
- Ministry of Colleges and Universities
- Natural Sciences and Engineering Research Council of Canada