Simulation of Josephson Junction Circuits With Only Ordinary Differential Equations

Superconducting electronics is a promising technology for many future computing solutions including superconducting digital processors, superconducting neuromorphic circuits, and superconducting quantum computing. Josephson junctions are at the heart of all of these, and the ability to simulate the dynamics of circuits of Josephson junctions is essential for the progress of these fields. The state-of-art software for simulating classical Josephson junction circuits represents their dynamics using a system of differential-algebraic equations (DAEs). Solving DAEs can lead to potentially erroneous outputs due to poor error control. Here, we present a method of simulating Josephson junction circuits based on graph theory that eliminates all algebraic equations to create a system of only ordinary differential equations (ODEs). This system of ODEs can be solved using a variable-step solver, which allows more precise error control.