Design of expressive and trainable pulse-based quantum machine learning models

Pulse-based quantum machine learning (QML) has emerged as a promising paradigm in quantum artificial intelligence due to its exceptional hardware efficiency. For real-world applications, it is crucial that pulse-based models are both expressive and trainable. Previous studies have shown that pulse-based models operating under dynamical symmetry can be effectively trained, benefiting from a favorable loss landscape devoid of barren plateaus. However, this approach may lead to uncontrollability, which can limit expressivity if the model is poorly designed. In this paper, we explore the conditions necessary for pulse-based QML models to maintain both expressivity and trainability. We present a key requirement involving the system's initial state, the measurement observable, and the underlying dynamical symmetry Lie algebra, supported by numerical simulations. Our results provide a comprehensive framework for the design of practical pulse-based QML models that strike a good balance between expressivity and trainability.