Thermodynamic Limits of Quantum Search
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Quantum Physics arXiv:2603.13654 (quant-ph) [Submitted on 13 Mar 2026] Title:Thermodynamic Limits of Quantum Search Authors:Ralf Riedinger View a PDF of the paper titled Thermodynamic Limits of Quantum Search, by Ralf Riedinger View PDF HTML (experimental) Abstract:Modern cryptography relies on keyed symmetric ciphers to ensure the secrecy and authenticity of high bandwidth data transfer. While the advent of quantum computers poses a challenge for public key cryptography, unbroken ciphers are considered safe against quantum attacks if their key is sufficiently long. However, concrete bounds on the required key length thus far remain elusive: Despite the well known asymptotic complexity of Grover's quantum search, the optimal algorithm to recover a secret key, no implementation-agnostic tight bounds were established. Here, we discuss the quantum thermodynamic limits of generic search algorithms, and find a work-runtime trade-off for autonomous computers with a fundamental lower bound. By devising an application-specific quantum protocol, which outperforms circuit and adiabatic implementations, and saturates this bound, we demonstrate that it is tight. Applying this limit, we find that a secret key of 831 bit length cannot be reconstructed deterministically in an expanding, dark-energy-dominated universe until star formation is expected to cease. Implications for post quantum cryptography, and quantum key distribution are discussed. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.13654 [quant-ph] (or arXiv:2603.13654v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2603.13654 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Ralf Riedinger [view email] [v1] Fri, 13 Mar 2026 23:30:35 UTC (34 KB) Full-text links: Access Paper: View a PDF of the paper titled Thermodynamic Limits of Quantum Search, by Ralf RiedingerView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-03 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?)