Tensor network modeling of chain modes in Josephson junction arrays

Josephson junction arrays are routinely used to create high-impedance lumped-element inductors. These components are central to qubit designs such as fluxonium and 0-π, as well as the Asymmetrically Threaded Squid (ATS) used in bosonic quantum error correction (QEC). Typically these many-body systems are treated with a single-mode approximation. However, this approximation can break down due to significant couplings between the low-energy manifold and the high-energy chain modes. In this talk, we address this challenge by using a nonperturbative method based on a variant of the density-matrix renormalization group, DMRG-X, to compute cross-Kerr nonlinearities while preserving the offset charge dependence of the array.