A Complete Equational Theory for Real-Clifford+CH Quantum Circuits
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910014213455872 |
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| author | Clément, Alexandre |
| author_facet | Clément, Alexandre |
| contents | We introduce a complete equational theory for the fragment of quantum circuits generated by the real Clifford gates plus the two-qubit controlled-Hadamard gate. That is, we give a simple set of equalities between circuits of this fragment, and prove that any other true equation can be derived from these. This is the first such completeness result for a finitely-generated, universal fragment of quantum circuits, with no parameterized gates and no need for ancillas. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_06644 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Complete Equational Theory for Real-Clifford+CH Quantum Circuits Clément, Alexandre Quantum Physics Logic in Computer Science We introduce a complete equational theory for the fragment of quantum circuits generated by the real Clifford gates plus the two-qubit controlled-Hadamard gate. That is, we give a simple set of equalities between circuits of this fragment, and prove that any other true equation can be derived from these. This is the first such completeness result for a finitely-generated, universal fragment of quantum circuits, with no parameterized gates and no need for ancillas. |
| title | A Complete Equational Theory for Real-Clifford+CH Quantum Circuits |
| topic | Quantum Physics Logic in Computer Science |
| url | https://arxiv.org/abs/2602.06644 |