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arXiv · 2604.02569

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

Brian García Sarmina·Guo-Hua Sun·Shi-Hai Dong
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Abstract

We introduce RFOX (Rotated-Field Oscillatory eXchange), a parameter-free quantum algorithm for combinatorial optimization that combines an almost constant non-stoquastic $XX$ catalyst with a weak harmonic $ZX$ counter-diabatic term. Using the Floquet-Magnus expansion, we derive an effective Hamiltonian whose leading-order $\mathcal{O}(\delta/\omega)$ corrections yield local $Y$ fields, field-modulated 2-body terms, and poly-local 3-body topological interactions driven by graph connectivity. This structure ensures a nearly flat instantaneous spectral gap, preventing the unpredictable gap collapses typical of conventional $X$ (stoquastic), $XX$, and $X+sXX$ (non-stoquastic) driver schedules. Extensive noiseless simulations and physical hardware experiments on IBM Quantum processors (up to 20 qubits) validate our spectral predictions. RFOX consistently attains near-optimal or exact ground states in the random-field Ising model using up to an order of magnitude fewer Trotter slices, with an advantage that grows alongside problem disorder. These results suggest that fixed-gap, non-stoquastic drivers augmented with analytically derived counter-diabatic terms offer a scalable, tuning-free route for quantum optimization.

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Brian García Sarmina, Guo-Hua Sun, Shi-Hai Dong. 2026-04-02. RFOX (Rotated-Field Oscillatory eXchange) quantum algorithm: Towards Parameter-Free Quantum Optimizers. https://arxiv.org/abs/2604.02569

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