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We first review, following our earlier studies, the critical behavior of thequantum Sherrington-Kirkpatrick (SK) model at finite as well as at zerotemperatures. Through the analysis of the Binder cumulant we determined theentire phase diagram of the model and from the scaling analysis of thenumerical data we obtained the correlation length exponent. For both thecritical Binder cumulant and the correlation length exponent, we observed acrossover from classical- to quantum-fluctuation-dominated values at a finitetemperature. We studied the behavior of the order parameter distribution of themodel in the glass phase (at finite and zero temperatures). Along with aclassical-fluctuation-dominated nonergodic region (where the replica symmetryis broken), we also found a quantum-fluctuation-dominated low-temperatureergodic region in the spin glass phase. In this quantum-fluctuation-dominatedregion, the order parameter distribution has a narrow peak around its mostprobable value, eventually becoming a delta function in theinfinite-system-size limit (indicating replica symmetry restoration orergodicity in the system). We also found that the annealing time (to reach avery low energy level of the classical SK model) becomes practicallysystem-size-independent when the annealing paths pass through this ergodicregion. In contrast, when such paths pass through the nonergodic region, theconvergence time grows rapidly with the system size. We present a new study ofthe autocorrelation of the spins in both ergodic and nonergodic regions. Wefound a significant increase in the relaxation time (and also a change in therelaxation behavior) in the classical-fluctuation-dominated (nonergodic) regioncompared with that in the quantum-fluctuation-dominated (ergodic) region of thespin glass phase.

On the Question of Ergodicity in Quantum Spin Glass Phase and its role in Quantum Annealing