Speaker
Description
The accurate numerical modeling of superconducting quantum devices is essential
for advanced computing and sensing technologies. Their governing equations are
nonlinear and often yield highly oscillatory solutions [1, 2], making standard time
integration schemes inaccurate unless very small time steps are used.
We consider a Backward Differentiation Formula (BDF) predictor-corrector method
enhanced through Exponential Fitting (EF) [3]. The idea is to incorporate physically
relevant parameters, such as damping factors and dominant frequencies, directly into
the discrete operator. The EF coefficients are obtained by imposing exactness of the
discrete derivative on a fitted functional space including exponential and oscillatory
modes, thus aligning the scheme with the qualitative behavior of the device.
This structure-aware discretization allows accurate simulations with larger time
steps, reducing computational effort and associated energy consumption while pre-
serving reliability. The approach is particularly effective in multi frequency regimes
typical of SQUID arrays and parametric amplifiers, where conventional solvers may
be overly restrictive.
Numerical tests on benchmark oscillatory problems and superconducting models
show improved accuracy at the same computational cost of standard BDF imple-
mentations, providing an efficient tool for the simulation and design of oscillatory
superconducting devices.
References
[1] N. D. Mermin, Quantum Computer Science: An Introduction, Cambridge Uni-
versity Press, 2007.
[2] C. Guarcello et al., Driving a Josephson Traveling Wave Parametric Amplifier
into chaos, Chaos, Solitons & Fractals, 189, 2024.
[3] L. Gr. Ixaru, Exponential Fitting, Kluwer Academic Publishers, 2004.