Proving the Limits of Quantum Power Flow

[2607.19263] Proving the Limits of Quantum Power Flow Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Quantum Physics arXiv:2607.19263 (quant-ph) [Submitted on 21 Jul 2026 ( v1 ), last revised 15 Aug 2026 (this version, v2)] Title: Proving the Limits of Quantum Power Flow Authors: Cameron Khanpour , Samuel Talkington View a PDF of the paper titled Proving the Limits of Quantum Power Flow, by Cameron Khanpour and Samuel Talkington View PDF HTML (experimental) Abstract: This letter proves realistic grid properties limit the applicability of quantum computers for power flow. Grids that split into two large regions meeting at only a few buses, common in transmission networks, force the pseudo condition number of the DC susceptance matrix to grow polynomially in the network size, and long chains of lines bridging such regions force quadratic growth. This rigorously verifies the empirical results of recent work. We also show that the theory holds without model information with high probability for independent bounded random line susceptances. Combined with query and tomography lower bounds, this precludes end-to-end quantum advantage for DC power flow at every readout level, and these obstructions persist through AC power flow, optimal power flow, and unit commitment. All proofs are formally verified in Lean 4. Subjects: Quantum Physics (quant-ph) ; Systems and Control (eess.SY) Cite as: arXiv:2607.19263 [quant-ph] (or arXiv:2607.19263v2 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2607.19263 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Cameron Khanpour [ view email ] [v1] Tue, 21 Jul 2026 16:36:17 UTC (11 KB) [v2] Sat, 15 Aug 2026 02:54:47 UTC (13 KB) Full-text links: Access Paper: View a PDF of the paper titled Proving the Limits of Quantum Power Flow, by Cameron Khanpour and Samuel Talkington View PDF HTML (experimental) TeX Source view license Current browse context: quant-ph < prev | next > new | recent | 2026-07 Change to browse by: cs cs.SY eess eess.SY References & Citations INSPIRE HEP NASA ADS Google 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? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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