Quantum Machine Learning for Complex Systems

TL;DR

This review discusses recent advances in quantum machine learning (QML) applied to complex systems, highlighting foundational paradigms, practical applications, and challenges in training, sampling, and scalability.

Contribution

It provides a comprehensive overview of QML techniques, their applications in complex quantum systems, and discusses new methods for improving scalability and trainability.

Findings

Neural-network quantum states effectively model correlated matter and dynamics.

Quantum-enhanced sampling improves scalability and learning diagnostics.

Hybrid quantum-classical frameworks are crucial for data-intensive applications.

Abstract

Quantum machine learning (QML) is rapidly transitioning from theoretical promise to practical relevance across data-intensive scientific domains. In this Review, we provide a structured overview of recent advances that bridge foundational quantum learning principles with real-world applications. We survey foundational QML paradigms, including variational quantum algorithms, quantum kernel methods, and neural-network quantum states, with emphasis on their applicability to complex quantum systems. We examine neural-network quantum states as expressive variational models for correlated matter, non-equilibrium dynamics, and open quantum systems, and discuss fundamental challenges associated with training and sampling. Recent advances in quantum-enhanced sampling and diagnostics of learning dynamics, including information-theoretic tools, are reviewed as mechanisms for improving scalability and trainability. The Review further highlights application-driven QML frameworks in drug discovery, cancer biology, and agro-climate modeling, where data complexity and constraints motivate hybrid quantum-classical approaches. We conclude with a discussion of federated quantum machine learning as a route to distributed, privacy-preserving quantum intelligence. Overall, this Review presents a unified perspective on the opportunities and limitations of QML for complex systems.