RFOX (Rotated-Field Oscillatory eXchange) quantum algorithm: Towards Parameter-Free Quantum Optimizers

Quantum Physics [Submitted on 2 Apr 2026] RFOX (Rotated-Field Oscillatory eXchange) quantum algorithm: Towards Parameter-Free Quantum Optimizers Brian García Sarmina, Guo-Hua Sun, Shi-Hai Dong 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: 20 pages, 14 figures 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 Submission history From: Brian García Sarmina PhD(c) [view email] [v1] Thu, 2 Apr 2026 22:44:10 UTC (13,654 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 Change to browse by: math math.OC References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation 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 Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)