# Collision model for non-Markovian quantum trajectories

## TL;DR

This paper introduces a collision model-based algorithm to simulate measurement-conditioned quantum trajectories in non-Markovian systems, accommodating different detection schemes and complex environmental memory effects.

## Contribution

It provides a novel algorithm for simulating non-Markovian quantum trajectories using collision models, applicable to various detection methods and environmental memory types.

## Key findings

- Successfully simulates trajectories with delayed feedback
- Handles systems with continuous environmental memory
- Adapts to photodetection and homodyne detection

## Abstract

We present an algorithm to simulate genuine, measurement-conditioned quantum trajectories for a class of non-Markovian systems, using a collision model for the environment. We derive two versions of the algorithm, the first corresponding to photodetection and the second to homodyne detection with a finite local oscillator amplitude. We use the algorithm to simulate trajectories for a system with delayed coherent feedback, as well as a system with a continuous memory.