Quantum circuit partition as a maze: emerging percolation transition via path finding
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Quantum Physics arXiv:2606.04070 (quant-ph) [Submitted on 2 Jun 2026] Title:Quantum circuit partition as a maze: emerging percolation transition via path finding Authors:P. Zentilini, M. Guatto, F. Preti, D. Arya, F. A. Cárdenas-López, F. Motzoi, E. Prati View a PDF of the paper titled Quantum circuit partition as a maze: emerging percolation transition via path finding, by P. Zentilini and 6 other authors View PDF HTML (experimental) Abstract:In quantum circuit optimization, circuit partitioning enables the optimization process to be parallelized across multiple devices. Each device is responsible for either reducing the number of selected gates or simplifying the local circuit structure. Most existing approaches to circuit partitioning are quantum-distribution-oriented and rely on splitting CNOT gates by introducing mid-circuit measurements and qubit resets. Currently, there is no criterion to determine how a circuit can be optimally partitioned without removing the CNOT gates for circuit optimization purposes. To address this challenge, we formalize the partition problem as a cutting path through a maze, where the CNOT gates represent the walls. We show that the existence of such a path separates quantum circuits into two classes through a percolation phase transition. In particular, it distinguishes a partitionable regime from a nonpartitionable one, arising from qubit permutations. Such permutations are generated by simulated annealing. We analyze its effect on the CNOT cluster from the perspective of network science and distribution analysis. Our results show that partitioning into two CNOT clusters is possible when the number of CNOTs is almost equal to the number of qubits. Based on this observation, we provide a scalable and practical criterion for identifying whether such a partition exists. Overall, our framework provides theoretical and numerical insight into circuit partitioning within quantum circuit optimization, forming the basis for algorithmic development. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2606.04070 [quant-ph] (or arXiv:2606.04070v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2606.04070 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Paolo Zentilini [view email] [v1] Tue, 2 Jun 2026 14:49:10 UTC (2,033 KB) Full-text links: Access Paper: View a PDF of the paper titled Quantum circuit partition as a maze: emerging percolation transition via path finding, by P. Zentilini and 6 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-06 References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: 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 Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)