Polynomial-time-scaling quantum dynamics with time-dependent quantum Monte Carlo

TL;DR

This paper introduces a polynomial-time quantum Monte Carlo method for simulating many-body quantum dynamics, effectively capturing correlations and responses in complex quantum systems.

Contribution

It develops a novel approach combining coupled Schrödinger equations and Monte Carlo walkers to reduce exponential scaling to polynomial time.

Findings

Accurately reproduces electron-pair densities in helium.

Predicts dipole response and ionization in strong optical fields.

Matches exact results for ultrashort pulse interactions.

Abstract

Here we study the dynamics of many-body quantum systems using time dependent quantum Monte Carlo method where the evolution is described by ensembles of particles and guide waves. The exponential-time scaling inherent to the quantum many-body problem is reduced to polynomial-time computation by solving concurrently a set of coupled Schroedinger equations for the guide waves in physical space and a set first order equations for the Monte Carlo walkers. We use effective potentials to accounts for the local and nonlocal quantum correlations in time-varying fields, where for fermionic states an exchange 'hole' is introduced explicitly through screened Coulomb potentials. The walker distributions for the ground states of para- and ortho-helium reproduce well the statistical properties, such as the electron-pair density function, of the real atoms. Our predictions for the dipole response and the ionization of an atom exposed to strong ultrashort optical pulse are in good agreement with the exact results.