A Quantum Phase-based Comparator

Quantum Physics arXiv:2609.25262 (quant-ph) [Submitted on 21 Sep 2026] Title:A Quantum Phase-based Comparator Authors:Alessandro Berti, Alessandro Poggiali View a PDF of the paper titled A Quantum Phase-based Comparator, by Alessandro Berti and Alessandro Poggiali View PDF HTML (experimental) Abstract:Quantum comparators decide the order of two operands. They rely on reversible logic acting on basis-encoded integers, so their width grows with the precision. We introduce the Quantum Phase-based Comparator (QPC), which compares two values carried in relative phases instead. The circuit places the two phases, entered with opposite signs, between a pair of Hadamard gates, and a fixed offset centers the interference, so that the probability of measuring zero falls below one half exactly when the first phase is the smaller. We give two implementations. With hard-coded values, the two values are written into the parameters of two phase gates, and the comparison costs one qubit and five gates. With the register-driven cascade, the values are drawn from two $t$-qubit registers through binary-weighted controlled-phase gates, at a cost of one qubit beyond the registers and depth linear in $t$; since the cascade induces each phase linearly from the register content, one circuit handles a superposition of operand pairs. The readout yields a biased coin rather than a definite bit, and we quantify the shots that a decision takes at a given phase separation. Scaling both phases by an integer widens the decision margin at no cost in width or depth, and an adaptive doubling schedule turns this amplification into a shot count logarithmic in the inverse separation. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2609.25262 [quant-ph] (or arXiv:2609.25262v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2609.25262 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Alessandro Berti [view email] [v1] Mon, 21 Sep 2026 18:12:56 UTC (91 KB) Full-text links: Access Paper: View a PDF of the paper titled A Quantum Phase-based Comparator, by Alessandro Berti and Alessandro PoggialiView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-09 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?)