Advanced Computational Methods for Quantum Devices

ABSTRACT Quantum computing relies on the accurate modeling of its fundamental components, many of which are based on superconducting technologies. Among these, Josephson junctions are of particular importance, as they play a crucial role in both qubit implementation and auxiliary technologies like parametric amplifiers \cite{AA, BB}. Accurately simulating such superconducting devices is a key challenge in computational physics, particularly in the study of quantum technologies. These amplifiers are essential for high-fidelity qubit readout and control, but their mathematical modeling involves nonlinear differential equations with highly oscillatory solutions, which standard numerical methods struggle to solve efficiently. A major difficulty in simulating these systems lies in the balance between numerical stability and accuracy. Traditional discretization techniques often require very fine time steps to simulate rapid oscillations, leading to excessive computational costs. This work introduces a computational technique based on exponential fitting theory \cite{CC} to address these difficulties. The proposed method adopts a predictor-corrector structure and incorporates prior knowledge of system characteristics, such as oscillation frequency and damping factors, to construct a suitable functional basis for numerical discretization. Numerical tests on highly oscillatory scenarios confirm the method’s effectiveness in capturing the intricate dynamics of Josephson junctions. The approach provides a valuable tool for improving the numerical modeling of superconducting circuits, contributing to the broader effort of refining simulation techniques in quantum computing. This is a joint work with Prof. C. Barone, A. Cardone, and S. Pagano from the University of Salerno.