Transforming Signs to Phase Distributions in Quantum Simulations

Abstract

A method is developed which speeds up averaging in quantum simulations where minus signs cause difficulties. A Langevin equation method in conjunction with a replication algorithm is used enabling one to average over a continuously varying complex number. Instead of ensemble averaging this number directly, the phase of the complex number is followed over time. The method is illustrated in some simple cases where the answers obtained can be compared to exact results, and also compared to conventional averaging procedures which converge orders of magnitude slower than this method. Limitations of this method are also described.