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

TL;DR

RFOX is a parameter-free quantum algorithm that uses a novel non-stoquastic driver to achieve near-optimal solutions efficiently, validated through simulations and hardware experiments.

Contribution

It introduces a new parameter-free quantum optimization method combining non-stoquastic drivers with counter-diabatic terms, ensuring a flat spectral gap and improved performance.

Findings

Achieves near-optimal ground states with fewer Trotter slices.

Validated by simulations and IBM Quantum hardware experiments.

Maintains a nearly flat spectral gap, preventing gap collapse.

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.