# Learning Hidden Quantum Markov Models

arXiv: https://arxiv.org/abs/1710.09016 · HTML: https://mlsanity.com/paper/1710.09016/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Oct 2017.

## Built on by (most cited first, 6 of 6)

- [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)
- [Streaming IoT Data and the Quantum Edge: A Classic/Quantum Machine Learning Use Case](https://mlsanity.com/paper/2402.15542/) (2024)
- [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)

Hidden Quantum Markov Models (HQMMs) can be thought of as quantum probabilistic graphical models that can model sequential data. We extend previous work on HQMMs with three contributions: (1) we show how classical hidden Markov models (HMMs) can be simulated on a quantum circuit, (2) we reformulate HQMMs by relaxing the constraints for modeling HMMs on quantum circuits, and (3) we present a learning algorithm to estimate the parameters of an HQMM from data. While our algorithm requires further optimization to handle larger datasets, we are able to evaluate our algorithm using several synthetic datasets. We show that on HQMM generated data, our algorithm learns HQMMs with the same number of hidden states and predictive accuracy as the true HQMMs, while HMMs learned with the Baum-Welch algorithm require more states to match the predictive accuracy.