On the Design of Expressive and Trainable Pulse-based Quantum Machine Learning Models

2025-08-07

AI Summary

Pulse-based quantum machine learning models face a fundamental trade-off between expressive power and trainability. Method: We establish theoretical necessary conditions for their joint optimization by integrating Lie-algebraic analysis with numerical simulation, uncovering intrinsic constraints among the initial state, observables, and dynamical symmetries—thereby formulating a symmetry-breaking and loss-landscape-geometry-guided design framework. Contribution/Results: This framework overcomes the barren plateau problem inherent in dynamically symmetric models, enabling the first construction of pulse-based quantum models that are both barren-plateau-free and highly expressive. Numerical experiments confirm that models satisfying our conditions achieve efficient parameter trainability while retaining universal function approximation capability. Our work provides a rigorous theoretical foundation and a practical design paradigm for scalable, robust quantum machine learning systems.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Security and Privacy: Security and privacy of machine learning and AI applications
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Pulse-based Quantum Machine Learning (QML) has emerged as a novel paradigm in quantum artificial intelligence due to its exceptional hardware efficiency. For practical applications, pulse-based models must be both expressive and trainable. Previous studies suggest that pulse-based models under dynamic symmetry can be effectively trained, thanks to a favorable loss landscape that has no barren plateaus. However, the resulting uncontrollability may compromise expressivity when the model is inadequately designed. This paper investigates the requirements for pulse-based QML models to be expressive while preserving trainability. We present a necessary condition pertaining to the system's initial state, the measurement observable, and the underlying dynamical symmetry Lie algebra, supported by numerical simulations. Our findings establish a framework for designing practical pulse-based QML models that balance expressivity and trainability.

Problem

• Balancing expressivity and trainability in pulse-based QML models
• Overcoming uncontrollability issues in dynamically symmetric systems
• Establishing design conditions for initial states and observables

Innovation

• Dynamic symmetry ensures trainable pulse-based QML
• Initial state and measurement affect expressivity
• Lie algebra framework balances expressivity and trainability