A Complete and Natural Rule Set for Multi-Qutrit Clifford Circuits
Fuente:
arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916911804055552 |
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| author | Li, Sarah Meng Mosca, Michele Ross, Neil J. van de Wetering, John Zhao, Yuming |
| author_facet | Li, Sarah Meng Mosca, Michele Ross, Neil J. van de Wetering, John Zhao, Yuming |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_14670 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Complete and Natural Rule Set for Multi-Qutrit Clifford Circuits Li, Sarah Meng Mosca, Michele Ross, Neil J. van de Wetering, John Zhao, Yuming Logic in Computer Science Quantum Physics 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. |
| title | A Complete and Natural Rule Set for Multi-Qutrit Clifford Circuits |
| topic | Logic in Computer Science Quantum Physics |
| url | https://arxiv.org/abs/2508.14670 |