Utilizing Discrete Variable Representations to Capture Phase Slips and Persistent-Current Vortices in Superconducting Circuits

The simulation of quantum superconducting circuits has become increasingly important for identifying system characteristics and modeling their relevant dynamics. Various numerical tools and packages have been developed with this purpose in mind, typically utilizing the harmonic oscillator basis and/or the charge basis to represent a Hamiltonian. In this work, we consider the use of discrete variable representations (DVRs) to construct a basis. In particular, we use so-called 'sinc DVRs' of both charge number and phase to approximate the eigenenergies of several prototypical examples, exploring their use and effectiveness in the numerical analysis of superconducting circuits. Our work suggests improvements in efficiency over standard approaches while offering a potential path to incorporating phase slips and persistent-current vortices in the simulation of superconducting circuits.