  We explore the behavior of order parameter distribution of quantum
Sherrington-Kirkpatrick model in the spin glass phase using Monte Carlo
technique for the effective Suzuki-Trotter Hamil- tonian at finite temperatures
and that at zero temperature obtained using exact diagonalization method. Our
numerical results indicate the existence of low but finite temperature quantum
fluc- tuation dominated ergodic region along with the classical fluctuation
dominated high temperature nonergodic region in the spin glass phase of the
model. In the ergodic region, the order parameter distribution gets narrower
around the most probable value of the order parameter as the system size
increases. In the other region, the Parisi order distribution function has
non-vanishing value every- where in thermodynamic limit, indicating
nonergodicity. We also show, that the average annealing time for convergence
(to a low energy level of the model; within a small error range) becomes system
size independent for annealing down through the (quantum fluctuation dominated)
ergodic region. It becomes strongly system size dependent for annealing through
the nonergodic region. Possible finite size scaling type behavior for the
extent of the ergodic region is also addressed.
