Control landscapes for superconducting transmon and fluxonium qubits

Quantum control plays an important role in the construction of quantum computing systems on the superconducting platform. Transmon and fluxonium are widely studied superconducting computing devices. This report examines the control analysis for the transmon and fluxonium superconducting systems using analytical and numerical methods. In this talk, for the transmon system we discuss the appearance of higher-order traps in the control landscape of maximizing average value of a quantum observable, and the criteria of strong regularity and complete controllability. For the fluxonium system, we outline the results of our numerical study, using the GRAPE algorithm, of control landscapes for quantum gates generation in the vicinity of the null control.