Robust Iterative Learning Hidden Quantum Markov Models

• URL: http://arxiv.org/abs/2510.23237v1
• Date: Mon, 27 Oct 2025 11:48:44 GMT
• Title: Robust Iterative Learning Hidden Quantum Markov Models
• Authors: Ning Ning,
• Abstract summary: Hidden Quantum Markov Models (HQMMs) extend classical Hidden Markov Models to the quantum domain.<n>Existing HQMM learning algorithms are sensitive to data corruption and lack mechanisms to ensure robustness under adversarial perturbations.<n>We introduce the Adversarially Corrupted HQMM, which formalizes robustness analysis by allowing a controlled fraction of observation sequences to be adversarially corrupted.
• Score: 0.7493761475572844
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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