Unleashing the Expressive Power of Pulse-Based Quantum Neural Networks
Han-Xiao Tao Jiaqi Hu Re-Bing Wu
Quantum machine learning (QML) based on Noisy Intermediate-Scale Quantum
(NISQ) devices requires the optimal utilization of limited quantum resources.
The commonly used gate-based QML models are convenient 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 coherence 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-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 show that the expressivity can be enhanced by either
increasing the pulse length or the number of qubits. As anticipated, we
demonstrate through numerical examples that the pulse-based model can unleash
more expressive power compared to the gate-based model. These findings
establish a theoretical foundation for understanding and designing expressive
QML models using NISQ devices.