Numerical computation of quantum dynamics is a key issue in the study of properties of solid state and modern quantum information technology systems. This paper presents an optimised method for calculating the coherent dynamics of a two-junction quantum superconductor interferometer based on the fourth-order Crank-Nicholson algorithm. There are considered supercomputer methods based on OpenMP technology and high-performance MKL libraries in different basises of a physical system. We demonstrate that there is an instantaneous basis to achieve optimized numerical modelling the system dynamics, which significantly reduces the dimensionality of the problem and reduces the absolute computational time.