Free Quantum Computing
Summarize this article with:
Quantum Physics arXiv:2602.16927 (quant-ph) [Submitted on 18 Feb 2026] Title:Free Quantum Computing Authors:Jacques Carette, Chris Heunen, Robin Kaarsgaard, Neil J. Ross, Amr Sabry View a PDF of the paper titled Free Quantum Computing, by Jacques Carette and 4 other authors View PDF HTML (experimental) Abstract:Quantum computing improves substantially on known classical algorithms for various important problems, but the nature of the relationship between quantum and classical computing is not yet fully understood. This relationship can be clarified by free models, that add to classical computing just enough physical principles to represent quantum computing and no more. Here we develop an axiomatisation of quantum computing that replaces the standard continuous postulates with a small number of discrete equations, as well as a free model that replaces the standard linear-algebraic model with a category-theoretical one. The axioms and model are based on reversible classical computing, isolate quantum advantage in the ability to take certain well-behaved square roots, and link to various quantum computing hardware platforms. This approach allows combinatorial optimisation, including brute force computer search, to optimise quantum computations. The free model may be interpreted as a programming language for quantum computers, that has the same expressivity and computational universality as the standard model, but additionally allows automated verification and reasoning. Comments: Subjects: Quantum Physics (quant-ph); Category Theory (math.CT) Cite as: arXiv:2602.16927 [quant-ph] (or arXiv:2602.16927v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2602.16927 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Journal reference: Proceedings of the National Academy of Sciences 123(8):e2510881123, 2026 Related DOI: https://doi.org/10.1073/pnas.2510881123 Focus to learn more DOI(s) linking to related resources Submission history From: Chris Heunen [view email] [v1] Wed, 18 Feb 2026 22:39:58 UTC (115 KB) Full-text links: Access Paper: View a PDF of the paper titled Free Quantum Computing, by Jacques Carette and 4 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-02 Change to browse by: math math.CT 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?) Links to Code Toggle Papers with Code (What is Papers with Code?) 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?)