ResQGRNN: Quantum-Compatible Residual Learning for Graph Recurrent Neural Networks

Quantum Graph Recurrent Neural Networks (QGRNNs) provide a powerful framework for learning sequential dependencies in quantum graph-based models. However, a significant challenge in advancing these networks lies in ensuring efficient trainability and scalability, as quantum systems inherently exhibit unique optimization difficulties. While residual learning has proven to be effective in classical deep learning for improving gradient flow and network convergence, integrating residual connections in quantum architectures is non-trivial due to the no-cloning theorem, which prevents the direct copying of quantum states. In this paper, we introduce Residual Quantum Graph Recurrent Neural Networks (ResQGRNNs), a novel approach that enhances the trainability of QGRNNs by incorporating residual connections while preserving quantum constraints. Unlike prior works that primarily focus on expressivity or classical datasets, our method directly addresses trainability concerns in quantum graph-based architectures. We propose an alternative strategy by using ancilla qubits to incorporate residual learning without violating quantum mechanical principles, ensuring effective parameter updates during training. Our results demonstrate that ResQGRNNs outperform the (plain) QGRNNs, leading to more stable optimization and enhanced performance on quantum graph learning tasks.