Generalization Error Bound for Quantum Machine Learning in NISQ Era - A Survey

2024-09-11

Quantum Machine Intelligence

AI Summary

Quantum machine learning (QML) in the NISQ era suffers from limited generalization due to hardware noise, yet existing generalization error theories rely on idealized assumptions and fail to incorporate realistic device constraints. Method: We conduct a Systematic Mapping Study (SMS) to unify and comparatively assess classical statistical learning bounds—including PAC and Rademacher complexity—in noisy quantum settings. Integrating quantum information theory with realistic noise-aware circuit modeling, we develop a generalization error framework tailored to intermediate-scale noisy quantum devices. Contribution/Results: We quantitatively characterize the coupling among noise strength, circuit depth, parameter count, and sample complexity. Deriving verifiable generalization upper bounds for over ten mainstream QML models—including VQE, QSVM, and QNN—we identify key hardware-induced bottlenecks to generalization and propose practically feasible optimization strategies.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• Security and Privacy: Security and privacy of machine learning and AI applications
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Problem

• Explores generalization error bounds for Quantum Machine Learning
• Analyzes QML performance in Noisy Intermediate-Scale Quantum era
• Summarizes quantum hardware platforms and optimization techniques

Innovation

• Quantum Machine Learning
• Generalization Error Bound
• Systematic Mapping Study