Breakdown of the Weak-Coupling Limit in Quantum Annealing
Yuki Bando, Ka-Wa Yip, Huo Chen, Daniel A. Lidar, Hidetoshi Nishimori · Physical Review Applied · 2022
Reverse annealing is a variant of quantum annealing, in which the system is prepared in a classical state, reverse annealed to an inversion point, and then forward annealed. We report on reverse annealing experiments using the D-Wave 2000Q device, with a focus on the p=2p -spin problem, which undergoes a second-order quantum phase transition with a gap that closes polynomially in the number of spins. We concentrate on the total and partial success probabilities, with the latter being the probabilities of finding each of two degenerate ground states of all spins up or all spins down, and the former being their sum. The empirical partial success probabilities exhibit a strong asymmetry between the two degenerate ground states, depending on the initial state of the reverse anneal. To explain these results, we perform open-system simulations using master equations in the limits of weak and strong coupling to the bath. The former, known as the adiabatic master equation, with decoherence in the instantaneous energy eigenbasis, predicts perfect symmetry between the two degenerate ground states, thus failing to agree with the experiment. In contrast, the latter, known as the polaron transformed Redfield equation, is in close agreement with experiment. Thus, our results present a challenge to the sufficiency of the weak system-bath coupling limit in describing the dynamics of current experimental quantum annealers, at least for reverse annealing on timescales of a microsecond or longer.