A practical, unitary simulator for non-Markovian complex processes

TL;DR

This paper introduces a finite-dimensional, unitary quantum simulator for discrete-time stochastic processes that uses less memory than classical models and avoids information loss, enabling potential experimental implementation.

Contribution

It presents a practical, finite-dimensional, unitary quantum simulation method for complex non-Markovian processes, improving memory efficiency over classical approaches.

Findings

Uses less internal memory than classical models

Operates unitarily to prevent information loss

Applicable to a broad class of stochastic processes

Abstract

Stochastic processes are as ubiquitous throughout the quantitative sciences as they are notorious for being difficult to simulate and predict. In this letter we propose a unitary quantum simulator for discrete-time stochastic processes which requires less internal memory than any classical analogue throughout the simulation. The simulator's internal memory requirements equal those of the best previous quantum models. However, in contrast to previous models it only requires a (small) finite-dimensional Hilbert space. Moreover, since the simulator operates unitarily throughout, it avoids any unnecessary information loss. We provide a stepwise construction for simulators for a large class of stochastic processes hence directly opening the possibility for experimental implementations with current platforms for quantum computation. The results are illustrated for an example process.