Unleashing the expressive power of pulse-based quantum neural networks

Abstract

Quantum machine learning (QML) based on Noisy Intermediate-Scale Quantum (NISQ) devices hinges on the optimal utilization of limited quantum resources. The broadly used gate-based QML models are user-friendly for software engineers, but their expressivity is restricted by the permissible circuit depth within a finite coherence time. In contrast, pulse-based models enable the construction of “infinitely” deep quantum neural networks within the same time, which may unleash greater expressive power for complex learning tasks. In this paper, we investigate this potential from the perspective of quantum control theory. We first indicate that the nonlinearity of pulse-based models comes from the encoding process that can be viewed as the continuous limit of data re-uploading in gate-based models. Subsequently, we prove that the pulse-based model can approximate arbitrary nonlinear functions when the underlying physical system is ensemble controllable. Under this condition, numerical simulations demonstrate the enhanced expressivity by increasing either the pulse length or the number of qubits. As anticipated, we show through numerical examples that the pulse-based model can unleash more expressive power compared to the gate-based model. These findings lay a theoretical foundation for understanding and designing expressive QML models using NISQ devices.