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

TL;DR

This paper explores how to design pulse-based quantum machine learning models that are both highly expressive and easily trainable, by establishing conditions on initial states, measurements, and symmetries.

Contribution

It introduces a necessary condition linking initial states, observables, and symmetries to ensure expressivity without sacrificing trainability in pulse-based QML.

Findings

Established a necessary condition for model expressivity and trainability.

Numerical simulations support the theoretical framework.

Provided guidelines for designing practical pulse-based QML models.

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 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.