Robust quantum-like state simulation using k-regular bipartite networks

We establish a framework for constructing robust quantum-like states based on k-regular bipartite graphs, aiming to realize quantum-inspired information processing through classical oscillatory networks. We first introduce the k-regular bipartite graph and its mathematical representation, and analyze its intrinsic spectral properties. In contrast to ordinary k-regular non-bipartite graphs, the intrinsic bipartite symmetry, enhanced spectral gap, and global delocalization mechanism confer superior robustness to the emergent states. We verify that the emergent states of these bipartite graphs satisfy the axiomatic requirements of quantum-like states, and show that the global delocalization property ensures stable operation under structural noise. Based on the axiomatic requirements of quantum-like states, we further realize basic quantum-inspired gate operations in the classical network framework. Our numerical simulations reveal that the k-regular bipartite graph system exhibits enhanced coherence and stability under noise interference compared with non-bipartite graph systems. This research not only broadens the application boundaries of quantum-inspired computing but also provides a new feasible path for the practical implementation of classical simulation of quantum information processing.