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

TL;DR

This study investigates how different pulse shapes affect qubit transition probabilities, combining theoretical models and experimental validation on IBM quantum hardware, revealing improved modeling accuracy and resonance frequency estimation.

Contribution

The paper introduces analytical expressions for transition probabilities for various pulse shapes, validated experimentally on IBMQ devices, enhancing understanding of pulse-shape effects in qubit dynamics.

Findings

Analytical models closely match experimental data.

Pulse-shape-dependent features are observed in transition profiles.

Improved accuracy in resonance frequency estimation using analytic models.

Abstract

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.