Implementing quantum dimensionality reduction for non-Markovian stochastic simulation

TL;DR

This paper demonstrates how quantum models can efficiently simulate complex non-Markovian systems with lower memory requirements than classical models, using a photonic setup to achieve higher precision with fewer resources.

Contribution

It introduces a practical implementation of quantum dimensionality reduction for non-Markovian processes, showing improved accuracy over classical models with equivalent memory.

Findings

Quantum models outperform classical models in accuracy.

Single-qubit quantum models require less memory.

Photonic setup successfully implements quantum stochastic simulations.

Abstract

Complex systems are embedded in our everyday experience. Stochastic modelling enables us to understand and predict the behaviour of such systems, cementing its utility across the quantitative sciences. Accurate models of highly non-Markovian processes -- where the future behaviour depends on events that happened far in the past -- must track copious amounts of information about past observations, requiring high-dimensional memories. Quantum technologies can ameliorate this cost, allowing models of the same processes with lower memory dimension than corresponding classical models. Here we implement such memory-efficient quantum models for a family of non-Markovian processes using a photonic setup. We show that with a single qubit of memory our implemented quantum models can attain higher precision than possible with any classical model of the same memory dimension. This heralds a key step towards applying quantum technologies in complex systems modelling.