The fast sampling algorithm for Lie-Trotter products

TL;DR

This paper introduces a fast, efficient algorithm for path sampling in path integral Monte Carlo simulations using Levy-Ciesielski Lie-Trotter products, achieving optimal computational cost.

Contribution

The paper presents a novel algorithm that leverages Levy-Ciesielski implementation to optimize path sampling efficiency with proven computational complexity.

Findings

Achieves computational cost of n*log_2(n) for path sampling.

Updating variables separately is more efficient than updating groups.

Demonstrates the optimality of the proposed sampling method.

Abstract

A fast algorithm for path sampling in path integral Monte Carlo simulations is proposed. The algorithm utilizes the Levy-Ciesielski implementation of Lie-Trotter products to achieve a mathematically proven computational cost of n*log_2(n) with the number of time slices n, despite the fact that each path variable is updated separately, for reasons of optimality. In this respect, we demonstrate that updating a group of random variables simultaneously results in loss of efficiency.