Analytically continued physical states in the path-integral: a sign-problem-free Quantum Monte Carlo simulation of Bell states dynamics

TL;DR

This paper introduces a sign-problem-free Monte Carlo method for simulating quantum states using analytically continued path integrals, enabling probabilistic sampling of Gaussian quantum systems and their influence on other systems.

Contribution

It demonstrates that path integrals can be deformed to produce probabilistic Gaussian integrals, providing a new practical algorithm for quantum simulations free of the sign problem.

Findings

Gaussian path integrals become probabilistic through domain deformation

Exact representation of Gaussian bath influence as classical non-Markovian noise

Connection between analytically continued path integrals and quasiprobability distributions

Abstract

The derivation of path integrals is reconsidered. It is shown that the expression for the discretized action is not unique, and the path integration domain can be deformed so that at least Gaussian path integrals become probabillistic. This leads to a practical algorithm of sign-problem-free Monte Carlo sampling from the Gaussian path integrals. Moreover, the dynamical influence of Gaussian quantum system (the bath) on any other quantum system can be exactly represented as interaction with classical non-Markovian noise. We discuss the relation of these findings to the Bell's theorem and the Feynman's conjecture on the exponential complexity of the classical simulation of quantum systems. In Feynman's path integral we have quasiprobability distributions for trajectories, and in analitycally continued path integrals we have probability distributions for quasitrajectories.