Double categories for adaptive quantum computation

Quantum Physics arXiv:2510.25915 (quant-ph) [Submitted on 29 Oct 2025] Title:Double categories for adaptive quantum computation Authors:Cihan Okay, Walker Stern, Redi Haderi, Selman Ipek View a PDF of the paper titled Double categories for adaptive quantum computation, by Cihan Okay and 3 other authors View PDF Abstract:Quantum computation can be formulated through various models, each highlighting distinct structural and resource-theoretic aspects of quantum computational power. This paper develops a unified categorical framework that encompasses these models and their interrelations using the language of double categories. We introduce double port graphs, a bidirectional generalization of port graphs, to represent the quantum (horizontal) and classical (vertical) flows of information within computational architectures. Quantum op- erations are described as adaptive instruments, organized into a one-object double category whose horizontal and vertical directions correspond to quantum channels and stochastic maps, respectively. Within this setting, we capture prominent adaptive quantum compu- tation models, including measurement-based and magic-state models. To analyze compu- tational power, we extend the theory of contextuality to an adaptive setting through the notion of simplicial instruments, which generalize simplicial distributions to double cat- egorical form. This construction yields a quantitative characterization of computational power in terms of contextual fraction, leading to a categorical formulation of the result that non-contextual resources can compute only affine Boolean functions. The frame- work thus offers a new perspective on the interplay between adaptivity, contextuality, and computational power in quantum computational models. Comments: Subjects: Quantum Physics (quant-ph); Category Theory (math.CT) Cite as: arXiv:2510.25915 [quant-ph] (or arXiv:2510.25915v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2510.25915 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Cihan Okay [view email] [v1] Wed, 29 Oct 2025 19:38:32 UTC (54 KB) Full-text links: Access Paper: View a PDF of the paper titled Double categories for adaptive quantum computation, by Cihan Okay and 3 other authorsView PDFTeX Source view license Current browse context: quant-ph new | recent | 2025-10 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?)