A New Way of Simulating Josephson Junction Circuits

Moore's law predicts the two-year doubling of transistor density on integrated circuits, but it has slowed down. In particular, the physical limits on the transistor size, heat dissipation by smaller transistors, and ascending demand for computing power send a clear note to the scientific community to develop more efficient computers. Superconducting digital, neuromorphic, or quantum computers have been promising solutions to the current challenges, and Josephson junction is at the heart of all of them. The state-of-art software for simulating Josephson junction circuits is WRSpice, which describes the circuits using differential-algebraic equations. The system can only be solved using a fixed-time step solver, leading to erroneous outputs due to insufficient resolution. We developed a new method of simulation based on graph theory that eliminates all algebraic equations and solves the system using a variable-time step solver, which allows more precise simulations of Josephson junction circuits.