Comparing Relaxation Mechanisms in Quantum and Classical Transverse-Field Annealing

Annealing schedule control provides opportunities to better understand the manner and mechanisms by which putative quantum annealers operate. By appropriately modifying the annealing schedule to include a pause (keeping the Hamiltonian fixed) for a period of time, we show that it is possible to more directly probe the dissipative dynamics of the system at intermediate points along the anneal and examine thermal relaxation rates, for example, by observing the repopulation of the ground state after the minimum spectral gap. We provide a detailed comparison of experiments from a D-Wave device, simulations of the quantum adiabatic master equation, and a classical analogue of quantum annealing, spin-vector Monte Carlo, and we observe qualitative agreement, showing that the characteristic increase in success probability when pausing is not a uniquely quantum phenomena. We find that the relaxation in our system is dominated by a single timescale, which allows us to give a simple condition for when we can expect pausing to improve the time to solution, the relevant metric for classical optimization. Finally, we also explore in simulation the role of temperature whilst pausing as a means to better distinguish quantum and classical models of quantum annealers.

Automated summary

Annealing schedule control allows for a better understanding of how putative quantum annealers operate, with the possibility to probe dissipative dynamics and thermal relaxation rates by modifying the annealing schedule. Experiments, simulations, and comparisons show that the increase in success probability when pausing is not uniquely quantum, and that relaxation in the system is dominated by a single timescale. Further exploration in simulation on the role of temperature during pausing helps distinguish between quantum and classical models of quantum annealers.