Predictive Performance of Deep Quantum Data Re-uploading Models

Quantum machine learning models incorporating data re-uploading circuits have garnered significant attention due to their exceptional expressivity and trainability. However, their ability to generate accurate predictions on unseen data, referred to as the predictive performance, remains insufficiently investigated. This study reveals a fundamental limitation in predictive performance when deep encoding layers are employed within the data re-uploading model. Concretely, we theoretically demonstrate that when processing high-dimensional data with limited-qubit data re-uploading models, their predictive performance progressively degenerates to near random-guessing levels as the number of encoding layers increases. In this context, the repeated data uploading cannot mitigate the performance degradation. These findings are validated through experiments on both synthetic linearly separable datasets and real-world datasets. Our results demonstrate that when processing high-dimensional data, the quantum data re-uploading models should be designed with wider circuit architectures rather than deeper and narrower ones.

Unleashing the Expressive Power of Pulse-Based Quantum Neural Networks

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.