Zero-variance principle for Monte Carlo algorithms

TL;DR

This paper introduces a zero-variance principle for Monte Carlo algorithms, providing a method to construct improved estimators that significantly reduce variance without additional computational cost, enhancing efficiency.

Contribution

It develops a general framework for creating optimal renormalized observables with minimal variance, applicable to classical and quantum Monte Carlo methods.

Findings

Method effectively reduces variance in Monte Carlo estimates.

Applicable to both classical and quantum Monte Carlo calculations.

Demonstrated power through multiple examples.

Abstract

We present a general approach to greatly increase at little cost the efficiency of Monte Carlo algorithms. To each observable to be computed we associate a renormalized observable (improved estimator) having the same average but a different variance. By writing down the zero-variance condition a fundamental equation determining the optimal choice for the renormalized observable is derived (zero-variance principle for each observable separately). We show, with several examples including classical and quantum Monte Carlo calculations, that the method can be very powerful.