# Single-shot quantum memory advantage in the simulation of stochastic processes

## TL;DR

This paper demonstrates a photonic quantum simulator that can encode stochastic processes more efficiently than classical methods, achieving a quantum memory advantage with a single simulator, not just in parallel scenarios.

## Contribution

First experimental demonstration of a quantum stochastic simulator with lower-dimensional encoding than classical counterparts, enabling practical memory savings.

## Key findings

- Quantum memory advantage achieved in a single simulator
- Photonic implementation of quantum stochastic simulation
- Reduced dimensionality in quantum encoding compared to classical

## Abstract

Stochastic processes underlie a vast range of natural and social phenomena. Some processes such as atomic decay feature intrinsic randomness, whereas other complex processes, e.g. traffic congestion, are effectively probabilistic because we cannot track all relevant variables. To simulate a stochastic system's future behaviour, information about its past must be stored and thus memory is a key resource. Quantum information processing promises a memory advantage for stochastic simulation that has been validated in recent proof-of-concept experiments. Yet, in all past works, the memory saving would only become accessible in the limit of a large number of parallel simulations, because the memory registers of individual quantum simulators had the same dimensionality as their classical counterparts. Here, we report the first experimental demonstration that a quantum stochastic simulator can encode the relevant information in fewer dimensions than any classical simulator, thereby achieving a quantum memory advantage even for an individual simulator. Our photonic experiment thus establishes the potential of a new, practical resource saving in the simulation of complex systems.