Robust Iterative Learning Hidden Quantum Markov Models

2025-10-27

AI Summary

Existing Hidden Quantum Markov Model (HQMM) learning algorithms exhibit high sensitivity to data contamination and lack formal robustness guarantees under adversarial perturbations. This paper formally defines the problem of robust HQMM learning under adversarial corruption. We propose a novel gradient-free iterative framework integrating entropy-driven denoising row filtering, stochastic resampling, L1-regularized likelihood optimization, and a physically constrained Kraus operator update mechanism—ensuring strict preservation of quantum complete positivity and trace preservation throughout model evolution. Evaluated across multiple HQMM and classical HMM benchmarks, our method significantly improves convergence stability, robustness against adversarial contamination, and adherence to quantum physical constraints, while achieving superior generalization performance compared to state-of-the-art approaches.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Intelligent Robots: State Estimation

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

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.

Problem

• Enhancing robustness of quantum models against data corruption
• Developing resilient learning algorithms for adversarial perturbations
• Ensuring physical validity in quantum sequential learning processes

Innovation

• Adversarially Corrupted HQMM formalizes robustness analysis
• RCR-EF module removes corrupted rows via entropy filtering
• L1-penalized likelihood objectives enhance stability and resist overfitting