# Robust Iterative Learning Hidden Quantum Markov Models

arXiv: https://arxiv.org/abs/2510.23237 · HTML: https://mlsanity.com/paper/2510.23237/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 19 references that are in the map.
- First posted on arXiv 27 Oct 2025.

## Builds on (most cited first, 7 of 7)

- [Multivariate Bayesian Structural Time Series Model](https://mlsanity.com/paper/1801.03222/) (2018)
- [Fast and robust quantum state tomography from few basis measurements](https://mlsanity.com/paper/2009.08216/) (2020)
- [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)
- [Learning and Inference in Hilbert Space with Quantum Graphical Models](https://mlsanity.com/paper/1810.12369/) (2018)
- [Iterated Block Particle Filter for High-dimensional Parameter Learning: Beating the Curse of Dimensionality](https://mlsanity.com/paper/2110.10745/) (2021)
- [Learning Circular Hidden Quantum Markov Models: A Tensor Network Approach](https://mlsanity.com/paper/2111.01536/) (2021)

## Built on by (most cited first, 1 of 1)

- [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) extend classical Hidden Markov Models to the quantum domain, offering a powerful probabilistic framework for modeling sequential data with quantum coherence. However, existing HQMM learning algorithms are highly sensitive to data corruption and lack mechanisms to ensure robustness under adversarial perturbations. In this work, we introduce the Adversarially Corrupted HQMM (AC-HQMM), which formalizes robustness analysis by allowing a controlled fraction of observation sequences to be adversarially corrupted. To learn AC-HQMMs, we propose the Robust Iterative Learning Algorithm (RILA), a derivative-free method that integrates a Remove Corrupted Rows by Entropy Filtering (RCR-EF) module with an iterative stochastic resampling procedure for physically valid Kraus operator updates. RILA incorporates L1-penalized likelihood objectives to enhance stability, resist overfitting, and remain effective under non-differentiable conditions. Across multiple HQMM and HMM benchmarks, RILA demonstrates superior convergence stability, corruption resilience, and preservation of physical validity compared to existing algorithms, establishing a principled and efficient approach for robust quantum sequential learning.