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 O(δ/ω) 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.