# Expressiveness and Learning of Hidden Quantum Markov Models

arXiv: https://arxiv.org/abs/1912.02098 · HTML: https://mlsanity.com/paper/1912.02098/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Dec 2019.

## Built on by (most cited first, 7 of 7)

- [Gradient-descent quantum process tomography by learning Kraus operators](https://mlsanity.com/paper/2208.00812/) (2022)
- [Memory compression and thermal efficiency of quantum implementations of non-deterministic hidden Markov models](https://mlsanity.com/paper/2105.06285/) (2021)
- [Learning Circular Hidden Quantum Markov Models: A Tensor Network Approach](https://mlsanity.com/paper/2111.01536/) (2021)
- [Identifiability and minimality bounds of quantum and post-quantum models of classical stochastic processes](https://mlsanity.com/paper/2509.03004/) (2025)
- [Robust Iterative Learning Hidden Quantum Markov Models](https://mlsanity.com/paper/2510.23237/) (2025)
- [A quantum learning approach based on Hidden Markov Models for failure scenarios generation](https://mlsanity.com/paper/2204.00087/) (2022)
- [Newton-Schulz Retraction-Based Inference Enables Hidden Quantum Markov Models to Outperform Classical HMMs](https://mlsanity.com/paper/2608.06554/) (2026)

## Abstract (arXiv)

Extending classical probabilistic reasoning using the quantum mechanical view of probability has been of recent interest, particularly in the development of hidden quantum Markov models (HQMMs) to model stochastic processes. However, there has been little progress in characterizing the expressiveness of such models and learning them from data. We tackle these problems by showing that HQMMs are a special subclass of the general class of observable operator models (OOMs) that do not suffer from the negative probability problem by design. We also provide a feasible retraction-based learning algorithm for HQMMs using constrained gradient descent on the Stiefel manifold of model parameters. We demonstrate that this approach is faster and scales to larger models than previous learning algorithms.