Unleashing the Expressive Power of Pulse-Based Quantum Neural Networks
This work addresses the problem of improving quantum machine learning performance for researchers and engineers using NISQ devices, offering a theoretical foundation for more expressive models, though it is incremental as it builds on existing quantum control theory.
The paper tackles the limited expressivity of gate-based quantum neural networks on NISQ devices by proposing pulse-based models, proving they can approximate arbitrary nonlinear functions under ensemble controllability and demonstrating enhanced expressivity through numerical simulations with increased pulse length or qubits.
Quantum machine learning (QML) based on Noisy Intermediate-Scale Quantum (NISQ) devices hinges on the optimal utilization of limited quantum resources. While gate-based QML models are user-friendly for software engineers, 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, this potential is investigated 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-reuploading 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 either increasing 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.