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.

翻译：隐量子马尔可夫模型（HQMMs）将经典隐马尔可夫模型扩展至量子领域，为具有量子相干性的序列数据建模提供了一个强大的概率框架。然而，现有的HQMM学习算法对数据损坏高度敏感，且缺乏在对抗性扰动下确保鲁棒性的机制。本文提出对抗性损坏隐量子马尔可夫模型（AC-HQMM），通过允许观测序列中受控比例的部分遭受对抗性损坏，从而形式化鲁棒性分析。为学习AC-HQMM，我们提出鲁棒迭代学习算法（RILA），这是一种无导数方法，它将基于熵过滤的损坏行移除模块与用于物理有效Kraus算子更新的迭代随机重采样过程相结合。RILA引入了L1惩罚似然目标，以增强稳定性、抵抗过拟合，并在不可微条件下保持有效性。在多个HQMM和HMM基准测试中，与现有算法相比，RILA展现出更优的收敛稳定性、损坏抵抗能力及物理有效性的保持，为鲁棒量子序列学习建立了一种原理清晰且高效的方法。