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

TL;DR

This paper studies how network-mediated capacitive couplings in superconducting transmon arrays affect operator scrambling and spectral properties, revealing rapid OTOC saturation and partial ergodicity beyond nearest-neighbor models.

Contribution

It demonstrates that increasing capacitive connectivity significantly alters dynamical and spectral behaviors in superconducting circuits, highlighting effects beyond traditional models.

Findings

OTOCs show accelerated operator scrambling with increased connectivity.

Spectral statistics shift from Poissonian towards level repulsion.

Behavior occurs within realistic superconducting device regimes.

Abstract

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.