# Time-local unraveling of non-Markovian stochastic Schr\"odinger equations

## TL;DR

This paper introduces a non-perturbative numerical method for solving non-Markovian stochastic Schr"odinger equations, making them more accessible and applicable in quantum mechanics research.

## Contribution

It proposes a novel approach to rewrite NMSSE as averages over auxiliary equations, enabling accurate simulations for both linear and non-linear cases.

## Key findings

- Provides a non-perturbative simulation algorithm for linear NMSSE.
- Extends method to non-linear NMSSE for isotropic complex noises.
- Enables direct sampling of norm-preserving NMSSE solutions.

## Abstract

Non-Markovian stochastic Schr\"odinger equations (NMSSE) are important tools in quantum mechanics, from the theory of open systems to foundations. Yet, in general, they are but formal objects: their solution can be computed numerically only in some specific cases or perturbatively. This article is focused on the NMSSE themselves rather than on the open-system evolution they unravel and aims at making them less abstract. Namely, we propose to write the stochastic realizations of linear NMSSE as averages over the solutions of an auxiliary equation with an additional random field. Our method yields a non-perturbative numerical simulation algorithm for generic linear NMSSE that can be made arbitrarily accurate for reasonably short times. For isotropic complex noises, the method extends from linear to non-linear NMSSE and allows to sample the solutions of norm-preserving NMSSE directly.