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 Schr\"odinger 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 same conjecture turns out to provide a very accurate
approximation for the Gaussian and exponential pulses too. The experimental
results are obtained with one of IBMQ'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
mean absolute error -- a measure of the accuracy of the fit -- features an
improvement by a factor of 4 to 8 for the analytic models compared to the
commonly used Lorentzian fits. Moreover, the uncertainty of the qubit's
resonance frequency is reduced by a factor of 4 for the analytic models
compared to the Lorentzian fits. These results demonstrate both the accuracy of
the analytic modelling of quantum dynamics and the excellent coherent
properties of IBMQ's qubit.
Ivo S. Mihov Nikolay V. Vitanov