  The efficiency of statistical sampling in broad-histogram Monte Carlo
simulations can be considerably improved by optimizing the simulated extended
ensemble for fastest equilibration. Here we describe how a recently developed
feedback algorithm can be generalized to find optimized sampling distributions
for the simulation of quantum systems in the context of the stochastic series
expansion (SSE) when defining an extended ensemble in the expansion order. If
the chosen update method is efficient, such as non-local updates for systems
undergoing a second-order phase transition, the optimized ensemble is
characterized by a flat histogram in the expansion order if a variable-length
formulation of the SSE is used. Whenever the update method suffers from
slowdown, such as at a first-order phase transition, the feedback algorithm
shifts weight towards the expansion orders in the transition region, resulting
in a non-uniform histogram.
