Closed-Form Optimal Quantum Circuits for Single-Query Identification of Boolean Functions
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Quantum Physics arXiv:2512.15901 (quant-ph) [Submitted on 17 Dec 2025] Title:Closed-Form Optimal Quantum Circuits for Single-Query Identification of Boolean Functions Authors:Leonardo Bohac View a PDF of the paper titled Closed-Form Optimal Quantum Circuits for Single-Query Identification of Boolean Functions, by Leonardo Bohac View PDF Abstract:We study minimum-error identification of an unknown single-bit Boolean function given black-box (oracle) access with one allowed query. Rather than stopping at an abstract optimal measurement, we give a fully constructive solution: an explicit state preparation and an explicit measurement unitary whose computational-basis readout achieves the Helstrom-optimal success probability 3/4 for distinguishing the four possible functions. The resulting circuit is low depth, uses a fixed gate set, and (in this smallest setting) requires no entanglement in the input state. Beyond the specific example, the main message is operational. It highlights a regime in which optimal oracle discrimination is not only well-defined but implementably explicit: the optimal POVM collapses to a compact gate-level primitive that can be compiled, verified, and composed inside larger routines. Motivated by this, we discuss a "what if" question that is open in spirit: for fixed (n,m,k), could optimal k-query identification (possibly for large hypothesis classes) admit deterministic, closed-form descriptions of the inter-query unitaries and the final measurement unitary acting on the natural n+m-qubit input--output registers (and, if needed, small work registers)? Even when such descriptions are not compact and do not evade known circuit-complexity barriers for generic Boolean functions, making the optimum constructive at the circuit level would be valuable for theory-to-hardware translation and for clarifying which forms of "oracle access" are physically meaningful. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2512.15901 [quant-ph] (or arXiv:2512.15901v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2512.15901 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Leonardo Bohac [view email] [v1] Wed, 17 Dec 2025 19:16:00 UTC (8 KB) Full-text links: Access Paper: View a PDF of the paper titled Closed-Form Optimal Quantum Circuits for Single-Query Identification of Boolean Functions, by Leonardo BohacView PDFTeX Source view license Current browse context: quant-ph new | recent | 2025-12 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?)