Numerical analysis of effective models for flux-tunable transmon systems

Simulations and analytical calculations that aim to describe flux-tunable transmons are usually based on effective models of the corresponding lumped-element model. However, when a control pulse is applied, in most cases it is not known how much the predictions made with the effective models deviate from the predictions made with the original lumped-element model. In this work we compare the numerical solutions of the time-dependent Schrödinger equation for both the effective and the lumped-element models, for various control pulses. We consider three different systems: a single flux-tunable transmon and two two-qubit systems. We find that a series of commonly applied approximations (individually and/or in combination) can change the response of a system substantially, when a control pulse is applied.