Lattice field theory for superconducting circuits

Accurately computing the properties of general, many-node superconducting circuits is challenging, since this requires solving the many-body Schrodinger equation. This work presents a new, ab-initio method for analyzing many-node superconducting circuits based on lattice field theory, a tool more commonly applied in nuclear and particle physics. The method is competitive with state-of-the-art techniques such as tensor networks, but avoids introducing systematic errors due to the truncation of the infinite-dimensional Hilbert space associated with superconducting phases. Example applications of the method to fluxonium are presented, where a systematic study of the influence of impedance & ground capacitances on fluxonium are explored. Many-body corrections to both lumped element circuit parameters and the coherent quantum phase slip rate are seen in the lattice data, and are used to formulate renormalized formulae incorporating these effects. The presented results are extracted from a statistical analyses of charge noise, where thousands of instantiations of charge disorder are explicitly averaged over at the microscopic level. Today this study would be difficult to achieve with any other existing method.