# Memory-efficient tracking of complex temporal and symbolic dynamics with quantum simulators

## TL;DR

This paper introduces a systematic quantum modeling protocol that efficiently simulates complex stochastic processes with less memory than classical models, broadening the scope of processes that can be modeled.

## Contribution

It extends quantum simulation methods to general temporal and symbolic dynamics using an elementary process description, overcoming classical limitations.

## Key findings

- Quantum models can simulate stochastic processes with less memory than classical models.
- The proposed protocol is broadly applicable to various types of dynamics.
- An example demonstrates an unbounded memory advantage of quantum over classical models.

## Abstract

Tracking the behaviour of stochastic systems is a crucial task in the statistical sciences. It has recently been shown that quantum models can faithfully simulate such processes whilst retaining less information about the past behaviour of the system than the optimal classical models. We extend these results to general temporal and symbolic dynamics. Our systematic protocol for quantum model construction relies only on an elementary description of the dynamics of the process. This circumvents restrictions on corresponding classical construction protocols, and allows for a broader range of processes to be modelled efficiently. We illustrate our method with an example exhibiting an apparent unbounded memory advantage of the quantum model compared to its optimal classical counterpart.