Numerical simulation of thermal noise in Josephson circuits

Abstract: We present a method to numerically add thermal noise to the equations of motion for a circuit of Josephson junctions. A new noise term, which we call "linearly interpolated Gaussian noise," replaces the usual white noise process. It consists of random noise values spaced at a chosen time interval and linearly interpolated in-between. This method can be used with variable time step solvers, allowing more precise control over the error while ensuring that fast dynamics are not missed by the solver. We derive the spectral density of such a noise term and compare it to a white noise process. Then we demonstrate the technique by computing the switching dynamics of a circuit of two Josephson junctions and comparing the results to the traditional method.