We published a new article that describes the independent nature of the Metropolis decision used in our pure-sampling quantum Monte Carlo algorithm. You can read it here.
Note: A pure-sampling quantum Monte Carlo algorithm with independent Metropolis
Jan Vrbik, Egor Ospadov and Stuart M. Rothstein
J. Chem. Phys. 145, 026101 (2016)
Recently, Ospadov and Rothstein published a pure-sampling quantum Monte Carlo algorithm (PSQMC) that features an auxiliary Path Z that connects the midpoints of the current and proposed Paths X and Y, respectively. When sufficiently long, Path Z provides statistical independence of Paths X and Y. Under those conditions, the Metropolis decision used in PSQMC is done without any approximation, i.e., not requiring microscopic reversibility and without having to introduce any G(x → x′; τ) factors into its decision function. This is a unique feature that contrasts with all competing reptation algorithms in the literature. An example illustrates that dependence of Paths X and Y has adverse consequences for pure sampling.