Data-driven Hamiltonian correction of transmon qubits

Abstract

We obtain correction terms for the standard Hamiltonian of 2 transmons driven by microwaves in cross-resonance. Data are obtained from a real transmon system, namely ibm_kyiv on the IBM quantum platform. Various data points obtained correspond to different microwave amplitudes and evolution times. We have an ansatz for the correction term and a correction operator whose matrix elements are parameters to be optimized for. We use adjoint sensitivity and gradient descent to obtain these parameters. Since the ansatz itself is not unique, we obtain an equivalence class of effective corrections through the methods we developed. We see a good fit in the predictions from the corrected Hamiltonian and hardware results. The average absolute error in predicting the resultant probability was reduced from a worst case value of 0.48 in the uncorrected Hamiltonian to below 0.05 in the correction, demonstrating the effectiveness of scientific machine learning for fine tuning theoretical models to faithfully reproduce observed data on time evolution multiple qubit systems.