RFOX (Rotated-Field Oscillatory eXchange) quantum algorithm: Towards Parameter-Free Quantum Optimizers
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Quantum Physics arXiv:2604.02569 (quant-ph) [Submitted on 2 Apr 2026] Title:RFOX (Rotated-Field Oscillatory eXchange) quantum algorithm: Towards Parameter-Free Quantum Optimizers Authors:Brian García Sarmina, Guo-Hua Sun, Shi-Hai Dong View a PDF of the paper titled RFOX (Rotated-Field Oscillatory eXchange) quantum algorithm: Towards Parameter-Free Quantum Optimizers, by Brian Garc\'ia Sarmina and 2 other authors View PDF HTML (experimental) Abstract:We introduce RFOX (Rotated-Field Oscillatory eXchange), a parameter-free quantum algorithm for combinatorial optimization. RFOX combines an almost constant non-stoquastic $XX$ catalyst with a weak harmonic $ZX$ counter-diabatic term. Using the Floquet-Magnus expansion, we derive a closed-form effective Hamiltonian whose first-order term retains the full $XX$ driver, while the leading correction consists of a single qubit $Y$ field at high drive frequency. This structure ensures that the instantaneous spectral gap remains essentially flat, independent of both the interpolation parameter and the disorder strength, modulated only by a $\delta$ parameter. This behavior stands in stark contrast to the unpredictable gap reductions, or even collapses, exhibited by the $X$ (stoquastic), $XX$, and $X+sXX$ (non-stoquastic) driver schedules. Extensive noiseless simulations on random-field Ising model (RFIM) instances with 7, 9, and 12 qubits, across three magnetic-field ranges, validate these spectral predictions: RFOX attains near-optimal, and in some cases exact, ground states using up to an order of magnitude fewer Trotter slices. Its performance advantage grows with increasing disorder, as conventional methods slow down near vanishing gaps, whereas RFOX maintains a constant runtime scaling of $T \propto \Delta_{\min}^{-2}$. Hardware experiments on IBM Quantum processors (Eagle r3 and Heron r1, with 12, 15, and 20 physical qubits) reproduce similar performance rankings. These results suggest that fixed-gap, non-stoquastic drivers augmented with analytically derived counter-diabatic terms offer a promising, scalable, and tuning-free route toward quantum optimizers for combinatorial optimization problems. Comments: Subjects: Quantum Physics (quant-ph); Optimization and Control (math.OC) MSC classes: 81P68, 68Q09, 68Q12 ACM classes: I.m; H.m Cite as: arXiv:2604.02569 [quant-ph] (or arXiv:2604.02569v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.02569 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Brian García Sarmina PhD(c) [view email] [v1] Thu, 2 Apr 2026 22:44:10 UTC (13,654 KB) Full-text links: Access Paper: View a PDF of the paper titled RFOX (Rotated-Field Oscillatory eXchange) quantum algorithm: Towards Parameter-Free Quantum Optimizers, by Brian Garc\'ia Sarmina and 2 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-04 Change to browse by: math math.OC 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?)