提出脉冲量子机器学习模型设计框架，兼顾表达力与可训练性。
On the Design of Expressive and Trainable Pulse-based Quantum Machine Learning Models
- 基于系统初态、测量可观测量与动力学对称李代数的关系，建立必要条件
- 数值模拟验证：满足条件的模型可避免平坦谷区，保持可训练性
- 适合研究量子算法设计与实用化量子机器学习的学者参考
脉冲基量子机器学习（QML）因其卓越的硬件效率成为量子人工智能的新范式。实际应用中，此类模型必须兼具表达力与可训练性。已有研究指出，在动态对称性下，脉冲模型可通过有利的损失景观实现有效训练，避免梯度消失问题。然而，若模型设计不当，这种可训练性可能以牺牲表达力为代价。本文系统探讨了脉冲基QML模型在保持可训练的同时具备表达力的设计要求。我们建立了关于系统初始态、测量可观测量及底层动力学对称性李代数之间的必要条件，并通过数值模拟加以验证。研究结果为设计兼具表达力与可训练性的实用脉冲基量子机器学习模型提供了理论框架。
原文摘要 · Abstract (English)
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 avoids 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 establish 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 provide a framework for designing practical pulse-based QML models that balance expressivity and trainability.
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