提出抗干扰的量子隐马尔可夫模型学习算法，提升量子序列建模鲁棒性。
Robust Iterative Learning Hidden Quantum Markov Models
- 设计无导数的迭代学习算法，结合熵滤波剔除污染数据
- 在多个基准上实现更稳定收敛与更强抗干扰能力
- 适合需要物理可行性保障的量子机器学习任务
隐量子马尔可夫模型（HQMM）将经典隐马尔可夫模型拓展至量子领域，为建模具有量子相干性的序列数据提供强大概率框架。然而，现有HQMM学习算法对数据污染高度敏感，缺乏应对对抗扰动的机制。本文提出对抗性污染隐量子马尔可夫模型（AC-HQMM），通过允许部分观测序列受控污染来形式化鲁棒性分析。为此，我们提出鲁棒迭代学习算法（RILA），一种无导数方法，融合基于熵过滤的污染行剔除（RCR-EF）模块与迭代随机重采样过程，实现物理有效的Kraus算子更新。RILA引入L1正则化似然目标以增强稳定性、抵抗过拟合并保持在非可微条件下的有效性。在多个HQMM与HMM基准测试中，RILA展现出优于现有算法的收敛稳定性、污染鲁棒性及物理有效性保持能力，确立了一种原则性强且高效的量子序列鲁棒学习方法。
原文摘要 · Abstract (English)
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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