Quantum Regularization through Holevo-Hayashi Information Bottleneck: A Single-Qubit Quantum Autoencoder for NISQ Devices

YIJIE ZHU, Richard Jiang

Keywords: Quantum Machine Learning, Quantum Neural Networks, Quantum Generative Model, Information Bottleneck, NISQ

Abstract: We introduce quantum regularization—a novel framework where generalization emerges naturally from quantum mechanical principles rather than explicit algorithmic design. Our approach integrates the Holevo-Hayashi Information Bottleneck (HHIB) with single-qubit quantum autoencoders, achieving superior performance through geometric constraints, measurement-induced stochasticity, and information-theoretic compression. Unlike classical approaches requiring dropout or weight decay, our quantum regularization framework leverages quantum mechanical constraints alone. We develop a resource-efficient single-qubit autoencoder using SU(2) group convolutions, achieving significant parameter efficiency while maintaining competitive reconstruction quality. Experiments, conducted on both classical simulators and IBM's quantum hardware, demonstrate consistent advantages over classical and quantum baselines. Our HHIB integration provides robust performance, validating its effectiveness for practical, NISQ-era deployment. This work establishes quantum regularization as a fundamental advantage of quantum learning systems, offering a new paradigm for resource-constrained quantum machine learning.

Primary Area: learning theory

Submission Number: 5113