Network-Mediated Capacitive Coupling Drives Fast OTOC Saturation in Superconducting Circuits

We investigate the dynamical and spectral consequences of capacitance-network-mediated interactions in superconducting transmon arrays beyond effective nearest-neighbor descriptions. While weak coupling regimes are well captured by an effective nearest-neighbor interacting models, we show that increasing capacitive connectivity induces a pronounced departure from this approximation in dynamical observables. Using Out-of-Time-Ordered Correlators (OTOCs), we demonstrate that such network-mediated couplings significantly accelerate operator scrambling, leading to rapid saturation compared to the nearest-neighbor limit. This dynamical crossover is accompanied by a shift in spectral statistics away from Poissonian behavior toward level repulsion, with the ratio parameter remaining intermediate between Poisson and Gaussian Orthogonal Ensemble (GOE) limits. This indicates the emergence of partial ergodicity rather than fully developed quantum chaos. As this behavior arises within experimentally realistic regimes of current superconducting transmon devices, identifying when network-mediated couplings qualitatively alter information dynamics is directly relevant for scalable superconducting architectures.

Source: arXiv:2605.05035v1 - http://arxiv.org/abs/2605.05035v1 PDF: https://arxiv.org/pdf/2605.05035v1 Original Link: http://arxiv.org/abs/2605.05035v1