Efficient equivalence checking of Clifford-U circuits with shared single-qubit unitaries

Quantum Physics [Submitted on 13 Mar 2026] Efficient equivalence checking of Clifford-U circuits with shared single-qubit unitaries Daisuke Sakamoto, Soshun Naito, Yusei Mori, Kosuke Mitarai Quantum circuit equivalence checking asks whether two circuits implement the same unitary. It guarantees compiler correctness and safe optimization, yet most existing approaches scale exponentially with the number of qubits or the circuit depth, or are restricted to specific circuit structures. In this work, we present an equivalence-checking method for circuits formed by arbitrary single-qubit layers interleaved with Clifford layers. This pattern is common in variational quantum algorithms and Hamiltonian simulation via Trotter decomposition. It can also represent any unitary with sufficient depth. We prove the existence of an efficient classical algorithm that determines whether a pair of circuits with shared single-qubit layers are equivalent for every possible choice of the shared single-qubit unitaries. The same algorithm can also certify their non-equivalence for fixed assignments of single-qubit unitaries. Our framework supports the validation of emerging quantum compilers and facilitate the discovery of novel circuit optimization passes. Comments: 15 pages, 3 figures Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.12697 [quant-ph]   (or arXiv:2603.12697v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.12697 Focus to learn more Submission history From: Daisuke Sakamoto [view email] [v1] Fri, 13 Mar 2026 06:25:26 UTC (503 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)