How to make quantum cheese: efficient geometry oracles for exponentially many pseudorandom microstructures
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Quantum Physics arXiv:2606.00222 (quant-ph) [Submitted on 29 May 2026] Title:How to make quantum cheese: efficient geometry oracles for exponentially many pseudorandom microstructures Authors:Alice Barthe View a PDF of the paper titled How to make quantum cheese: efficient geometry oracles for exponentially many pseudorandom microstructures, by Alice Barthe View PDF Abstract:Quantum algorithms for simulating linear systems are often formulated under oracle access assumptions. A central question is when such oracles can be implemented by polynomial-size quantum circuits. In this paper, we study this question for materials specified by rules rather than by exhaustive descriptions. We focus on textured materials with exponentially many geometric features. In two settings, we show that, without additional structure, describing such geometries yields Grover-type lower bounds, making the corresponding quantum oracles intractable in general. In contrast, when suitable structure is imposed, we identify a broad family of pseudorandom locally textured materials whose geometry can be queried through a polynomial-size quantum circuit. We provide explicit circuit constructions for these oracles and verify their behaviour through numerical simulation. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2606.00222 [quant-ph] (or arXiv:2606.00222v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2606.00222 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Alice Barthe [view email] [v1] Fri, 29 May 2026 18:00:15 UTC (217 KB) Full-text links: Access Paper: View a PDF of the paper titled How to make quantum cheese: efficient geometry oracles for exponentially many pseudorandom microstructures, by Alice BartheView PDFTeX 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?)