Magnetic Memory and Hysteresis from Quantum Transitions: 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 robust hysteresis in large-scale transverse-field Ising systems implemented on D-Wave's analog quantum hardware. The quantum nature of these intriguing results remains to be understood at a deeper level. Here, we present a conceptual framework that explains the observed behavior by combining two-level Landau-Zener transitions via a first-order piecewise-constant propagator with semiclassical domain-wall kinetics. We test this approach experimentally on a quantum annealer, where we observe clear coercivity even in one-dimensional rings with periodic boundary conditions comprising up to 4,906 qubits-regimes where classical hysteresis is forbidden, but quantum hysteresis is not. Our framework reproduces the measured kink densities, hysteresis loop shapes, and longitudinal sweep-rate scaling trends observed in data from three different D-Wave quantum annealers. In particular, it captures striking non-monotonic features and transiently negative susceptibilities, identifying them as genuine quantum memory effects. These results establish programmable quantum annealers as powerful testbeds for exploring memory-endowed non-equilibrium dynamics in quantum many-body systems.