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

arXiv: https://arxiv.org/abs/2105.06285 · HTML: https://mlsanity.com/paper/2105.06285/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 78 references that are in the map.
- First posted on arXiv 13 May 2021.

## Builds on (most cited first, 3 of 3)

- [Expressiveness and Learning of Hidden Quantum Markov Models](https://mlsanity.com/paper/1912.02098/) (2019)
- [Learning Hidden Quantum Markov Models](https://mlsanity.com/paper/1710.09016/) (2017)
- [Leveraging Environmental Correlations: The Thermodynamics of Requisite Variety](https://mlsanity.com/paper/1609.05353/) (2016)

## Built on by (most cited first, 4 of 4)

- [Quantum adaptive agents with efficient long-term memories](https://mlsanity.com/paper/2108.10876/) (2021)
- [Learning Circular Hidden Quantum Markov Models: A Tensor Network Approach](https://mlsanity.com/paper/2111.01536/) (2021)
- [Accuracy vs Memory Advantage in the Quantum Simulation of Stochastic Processes](https://mlsanity.com/paper/2312.13473/) (2023)
- [Identifiability and minimality bounds of quantum and post-quantum models of classical stochastic processes](https://mlsanity.com/paper/2509.03004/) (2025)

## Abstract (arXiv)

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.