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

TL;DR

This work investigates how pulse shape influences the detuning-dependent qubit transition probability $P_{0\rightarrow 1}(\Delta)$ by experimentally validating analytic models for five envelopes (rectangular, Gaussian, hyperbolic secant, sech^2, exponential) on an IBM Quantum processor. It combines exact or approximate solutions (Rabi, Rosen-Zener, Demkov) with a Rosen-Zener-based conjecture to capture off-resonant behavior, showing that these analytic descriptions outperform Lorentzian fits in MAE and resonance-frequency uncertainty. Correcting for dephasing, readout, and leakage, the study demonstrates that analytic models achieve 4–8× reductions in MAE and 4× reductions in resonance-frequency variance across most shapes, while Gaussian, exponential, and sech^2 pulses are well described by the augmented Rosen-Zener framework. The results validate precise quantum-dynamics modeling with real hardware, with practical implications for improved gate calibration and fidelity, and are expected to generalize across platforms beyond the transmon-based IBM device.

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 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 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.

Figures (5)

• Figure 1: (Colour online) The transition line profile for the Rabi model: measured data (black crosses), fit using the Rabi formula in Eq. \ref{['eq-rabi']} (red) and a Lorentzian $L = A/(1 + (k\Delta^2)) + C$ curve (blue) for comparison, where $k$ is a free fitting parameter.
• Figure 2: (Colour online) The transition line profile for the Rosen-Zener model: measured data (black crosses), fit using the Rosen-Zener formula in Eq. \ref{['eq-rz']} (red) and a Lorentzian curve (blue) for comparison.
• Figure 3: (Colour online) The transition line profile for the exponential Demkov model: measured data (black crosses), fit using the analytic formula with the Bessel functions Eq. \ref{['eq-demkov']} (red), the formula derived from the Rosen-Zener conjecture Eq. \ref{['eq-demkov-rzc']} (green) and a Lorentzian curve (blue) for comparison.
• Figure 4: (Colour online) The transition line profile for the Gaussian model: measured data (black crosses), fit using the Gaussian model DDP formula in Eq. \ref{['eq-gauss']} (red), the Gaussian RZC model (green), and a Lorentzian curve (blue) for comparison.
• Figure 5: (Colour online) The transition line profile for the sech$^2$ model: measured data (black crosses), fit using the sech$^2$ model formula (Eq. \ref{['eq-sech2']}) (red) and a Lorentzian curve (blue) for comparison.