Magnetic memory and hysteresis from quantum transitions in theory and experiments on quantum annealers

Abstract Quantum annealing leverages quantum tunneling for non-local searches, thereby minimizing memory effects that typically arise from metastabilities. Nonetheless, recent work has demonstrated protocols for robust hysteresis in large-scale transverse-field Ising systems on D-Wave quantum hardware. The quantum nature of these results remains to be understood, and existing theoretical approaches fail to capture the observed phenomenology in the far-from-equilibrium regime of driven longitudinal fields. Here, we present a hybrid framework that interleaves low-order Landau-Zener transitions with semiclassical domain wall kinetics, coupling the two channels through an iterative proportional fitting procedure that captures decoherence and measurement without requiring an explicit open-system model. Validated on three D-Wave annealers, the framework reproduces measured hysteresis loops, non-monotonic magnetization reversals, and transiently negative susceptibilities in rings of up to 4,906 qubits, and yields analytic scaling predictions for defect density and hysteresis area confirmed by experiment. These results establish programmable quantum annealers as platforms for exploring memory and non-equilibrium dynamics in driven quantum many-body systems.