Extreme dimensionality reduction with quantum modelling

TL;DR

This paper demonstrates that quantum models can drastically reduce the memory needed for forecasting certain complex stochastic processes, outperforming classical models by using only a qubit.

Contribution

It introduces a family of processes where quantum models achieve maximal compression, storing all relevant past information in just a single qubit, unlike classical models.

Findings

Quantum models can store all relevant information in a single qubit.

Classical models require unbounded memory for these processes.

Quantum compression offers practical advantages for forecasting complex systems.

Abstract

Effective and efficient forecasting relies on identification of the relevant information contained in past observations -- the predictive features -- and isolating it from the rest. When the future of a process bears a strong dependence on its behaviour far into the past, there are many such features to store, necessitating complex models with extensive memories. Here, we highlight a family of stochastic processes whose minimal classical models must devote unboundedly many bits to tracking the past. For this family, we identify quantum models of equal accuracy that can store all relevant information within a single two-dimensional quantum system (qubit). This represents the ultimate limit of quantum compression and highlights an immense practical advantage of quantum technologies for the forecasting and simulation of complex systems.