Memory compression and thermal efficiency of quantum implementations of non-deterministic hidden Markov models

TL;DR

This paper develops quantum implementations of non-deterministic hidden Markov models, demonstrating they can reduce thermal dissipation and improve memory efficiency compared to classical models, thus broadening quantum advantages in stochastic modeling.

Contribution

It provides a systematic method for constructing quantum non-deterministic HMMs that restore quantum advantages in memory and thermal efficiency.

Findings

Quantum non-deterministic HMMs mitigate thermal dissipation.

Quantum implementations achieve better memory compression.

Advantages extend beyond deterministic HMMs to broader classes.

Abstract

Stochastic modelling is an essential component of the quantitative sciences, with hidden Markov models (HMMs) often playing a central role. Concurrently, the rise of quantum technologies promises a host of advantages in computational problems, typically in terms of the scaling of requisite resources such as time and memory. HMMs are no exception to this, with recent results highlighting quantum implementations of deterministic HMMs exhibiting superior memory and thermal efficiency relative to their classical counterparts. In many contexts however, non-deterministic HMMs are viable alternatives; compared to them the advantages of current quantum implementations do not always hold. Here, we provide a systematic prescription for constructing quantum implementations of non-deterministic HMMs that re-establish the quantum advantages against this broader class. Crucially, we show that whenever the classical implementation suffers from thermal dissipation due to its need to process information in a time-local manner, our quantum implementations will both mitigate some of this dissipation, and achieve an advantage in memory compression.