Quantum coarse-graining for extreme dimension reduction in modelling stochastic temporal dynamics

TL;DR

This paper introduces a quantum coarse-graining method that significantly reduces the memory dimension needed for modeling stochastic temporal dynamics, enabling efficient, high-fidelity quantum simulations of complex systems.

Contribution

It presents a novel lossy quantum coarse-graining technique that drastically decreases memory requirements without sacrificing temporal resolution.

Findings

Memory dimension reduced by quantum coarse-graining

Maintains near-exact statistical fidelity

Enables practical quantum stochastic modeling

Abstract

Stochastic modelling of complex systems plays an essential, yet often computationally intensive role across the quantitative sciences. Recent advances in quantum information processing have elucidated the potential for quantum simulators to exhibit memory advantages for such tasks. Heretofore, the focus has been on lossless memory compression, wherein the advantage is typically in terms of lessening the amount of information tracked by the model, while -- arguably more practical -- reductions in memory dimension are not always possible. Here we address the case of lossy compression for quantum stochastic modelling of continuous-time processes, introducing a method for coarse-graining in quantum state space that drastically reduces the requisite memory dimension for modelling temporal dynamics whilst retaining near-exact statistics. In contrast to classical coarse-graining, this compression is not based on sacrificing temporal resolution, and brings memory-efficient, high-fidelity stochastic modelling within reach of present quantum technologies.