Pulse shape effects in qubit dynamics demonstrated on an IBM quantum computer

We present a study of the coherent interaction of a qubit with a pulse-shaped external field of a constant carrier frequency. We explore, theoretically and experimentally, the transition line profile -- the dependence of the transition probability on the detuning -- for five different pulse shapes: rectangular, Gaussian, hyperbolic-secant, squared hyperbolic-secant and exponential. The theoretical description for all cases but sech$^2$ is based on the analytical solutions to the Schrödinger equation or accurate approximations available in the literature. For the sech$^2$ pulse we derive an analytical expression for the transition probability using the Rosen-Zener conjecture, which proves very accurate. The experimental results are obtained with one of IBM's quantum processors. An excellent agreement between theory and experiment is observed, demonstrating some pulse-shape-dependent fine features of the transition probability profile. The divergence index -- a measure of the accuracy of the fit -- features an improvement by a factor of 4 to 7 for the analytic models compared to the commonly used (sinc$^2$ and Lorentzian) baseline fits. Moreover, we observe a reduction by about a factor of about 4 of the error bars of the resonance frequency of the qubit for the analytic models compared to the baseline fits. These results demonstrate both the accuracy of the analytic modelling of quantum dynamics and the excellent coherent properties of IBM's qubit.