Robust Iterative Learning Hidden Quantum Markov Models

TL;DR

This paper introduces a robust learning algorithm for Hidden Quantum Markov Models that withstands adversarial data corruption, improving stability and physical validity in quantum sequential data modeling.

Contribution

The paper proposes the RILA algorithm with entropy filtering and L1-penalized likelihood for robust, stable HQMM learning under adversarial corruption.

Findings

RILA outperforms existing algorithms in convergence stability.

RILA effectively resists data corruption and maintains physical validity.

The method demonstrates superior performance on HQMM and HMM benchmarks.

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.