Pulse shape effects in qubit dynamics demonstrated on an IBM quantum computer
Abstract
We present a study of the coherent interaction of a qubit with a pulseshaped 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, hyperbolicsecant, squared hyperbolicsecant 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 RosenZener 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 pulseshapedependent 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.
 Publication:

arXiv eprints
 Pub Date:
 January 2023
 DOI:
 10.48550/arXiv.2301.10004
 arXiv:
 arXiv:2301.10004
 Bibcode:
 2023arXiv230110004M
 Keywords:

 Quantum Physics
 EPrint:
 10 pages including appendix and references, 5 figures