# Real-time Diffusion Monte Carlo method

## TL;DR

This paper introduces a novel real-time Diffusion Monte Carlo method that can handle complex distributions by making them piecewise positive, enabling the study of quantum systems' dynamics and excited states.

## Contribution

The authors demonstrate a new approach to real-time diffusion Monte Carlo that overcomes previous limitations by transforming complex distributions into positive ones, allowing for broader quantum simulations.

## Key findings

- Successfully applied to the 1D harmonic oscillator
- Can find ground and excited states
- Potential to locate wave function nodes in fermionic systems

## Abstract

Direct sampling of multi-dimensional systems with quantum Monte Carlo methods allows exact account of many-body effects or particle correlations. The most straightforward approach to solve the Schr\"odinger equation, Diffusion Monte Carlo, has been used in several benchmark cases for other methods to pursue. Its robustness is based on direct sampling of a positive probability density for diffusion in imaginary time. It has been argued that the corresponding real time diffusion can not be realised, because the corresponding oscillating complex valued distribution can not be used to drive diffusion. Here, we demonstrate that this can be done with a couple of tricks turning the distribution piecewise positive and normalisable. This study is a proof of concept demonstration using the well-known and transparent case: one-dimensional harmonic oscillator. Furthermore, we show that our novel method can be used to find not only the ground state but also excited states and even the time evolution of a given wave function. Considering fermionic systems, this method may turn out to be feasible for finding the wave function nodes.