Problem

The rapid growth of AI and deep learning has spurred innovation in neuromorphic computing and quantum machine learning. However, existing Spiking Quantum Neural Network (SQNN) implementations often rely on pre-trained Spiking Neural Networks (SNNs) due to the non-differentiable nature of spiking activity and limitations in SNN encoder scalability. A significant gap exists in providing a comprehensive theoretical framework and systematic benchmarking for these hybrid models under various training conditions. Furthermore, the development of powerful quantum neural networks is hindered by current quantum hardware limitations, including decoherence, noise, and the "barren plateau" problem, which particularly affect Noisy Intermediate-Scale Quantum (NISQ) devices and restrict the scalability of quantum circuits.

Method

This work proposes the Spiking-Quantum Data Re-upload Convolutional Neural Network (SQDR-CNN), a novel architecture that integrates spiking convolutional layers with a quantum data re-uploading classifier. The SNN encoder utilizes standard convolutional layers, batch normalization, max pooling, and adaptive pooling to extract features from images. These spiking layers are trained using surrogate gradients, specifically employing the arctan surrogate function for effective backpropagation. The quantum component is a Parameterized Quantum Circuit (PQC) based on a quantum data re-uploading framework, constructed by stacking multiple data re-upload (DR) blocks that use Rot gates and circularly entangled controlled-Z (CZ) gates. The paper also theoretically and empirically justifies the inclusion of a classical Multi-Layer Perceptron (MLP) after the PQC, demonstrating that it enhances model expressivity, rescales quantum gradients, and helps mitigate the barren plateau phenomenon. Experiments were conducted using PyTorch, SpikingJelly for SNNs, and PennyLane for quantum circuit simulations, including both noiseless and noisy environments. Training involved the Adam optimizer, cross-entropy loss, image normalization, horizontal random flips for augmentation, and a phase coding scheme for spike-based encoding.

Results

The SQDR-CNN variants demonstrated competitive performance while drastically reducing parameter counts compared to state-of-the-art SNN baselines. For instance, on the MNIST dataset, the SQDR-CNN[4b-18q] model achieved approximately 86% of the accuracy of the top-performing SOTA SNN (PLIF at 99.72%) but used only 0.5% of the parameters of the smallest SOTA model (LISNN), representing a 99.5% reduction. The SQDR-CNN also consistently outperformed Spiking-ResNet variants across different datasets, with accuracy gaps ranging from 6.59% to 73.92%. While a performance drop was observed on Fashion-MNIST (78% of PLIF's accuracy with 99.7% parameter reduction), the significant model size compression across all datasets highlights the architecture's efficiency. Under noisy simulated quantum environments (bit-flip, depolarizing, and amplitude damping errors), the SQDR-CNN[4b-9q] variant experienced the most substantial performance degradation, suggesting that deep PQCs with limited qubits are less effective on NISQ devices. However, the SQDR-CNN[4b-18q] variant, with more trainable parameters, showed significantly mitigated performance impact under noise, emphasizing the importance of balancing PQC depth and qubit count. The Adam optimizer consistently yielded the best performance, and a truncated normal distribution U(0, 2π) for PQC initialization resulted in the highest average accuracy, correlating with higher mean gradient variance and slower decay, which helps address barren plateaus.

Implications

The proposed SQDR-CNN represents a significant step forward in hybrid spiking-quantum architectures, offering a parameter-efficient model capable of end-to-end optimization. Its ability to achieve competitive performance with considerably fewer parameters than traditional SNNs opens new avenues for research in multi-modal, learnable systems, particularly for resource-constrained applications. The extensive evaluation under various conditions, including noisy quantum circuits, different initialization settings, and optimization algorithms, provides a valuable reference for future research in this emerging field. However, the study also highlights current limitations, such as the trade-off between PQC size and classification accuracy, and challenges in scaling under noise. Future work should focus on developing more efficient PQC architectures, robust scaling strategies to mitigate gradient vanishing, and noise-resilient circuit templates. Crucially, validation on actual quantum hardware platforms and benchmarking against other specialized parameter-efficient AI models will be essential to establish the real-world applicability and scalability of hybrid spiking-quantum systems.