Harmonic driving and dynamic transitions in the Landau–Zener–Stückelberg–Majorana interferometry induced by tunneling flux-driven symmetric transmon qubits

Abstract

In this study, Landau–Zener–Stückelberg–Majorana (LZSM) dynamics of tunneling transmon quantum bits (qubits) and related interference effects (interferometry) in symmetrical Josephson junctions (JJs) are theoretically investigated. Accordingly, the deviation of the driving parameters from the symmetry point and the transmon frequency are introduced, leading to fluctuations of a superconducting gap that limit the computational power of state-of-the-art transmon qubits and micro-processors. Indeed, the theoretical approach is carried withing the framework of the dynamic matrix approach (DMA) and numerical experiment measurements are reported after both single and double passages through a complexity of the transmon qubit polarization energy. Therefore, we derive generalized analytical expressions of LZSM quantum tunneling probabilities (QTP) and energy eigenvalues for multiple passages processes, which allow us to efficiently establish the transmon frequency and determine the driving parameters. Our theoretical results seem relevant for the interpretation of several LZSM interferometry mechanisms in the modulation of superconducting gap through different transmon qubit spectroscopy experiments in which tunable LZSM transitions and quantum interference patterns are demonstrated by the use of universal nonadiabatic control to implement quantum emulations. Additionally, this mapping enables the investigation of JJ effects through the identification of the corresponding modulated topological phases accumulated during the LZSM transitions, which offer new opportunities to coherently manipulate qubit states and address the energy transfer of transmon qubits on the one hand. On the other hand, it suggests possibilities to reduce sensitivity and to suspected sources of imperfection from different superconducting qubit architectures, particularly in the context of materials optimization strategies that dig out nontrivial phenomena possessing powerful quantum interferometer functionality with realistic quantum controls of tunneling transmon qubit states. • Dynamics of tunneling transmon qubits and the interference effects through a complexity of the transmon polarization energy. • Control of superconducting gap fluctuations through the energies and the transition probabilities spectroscopy. • Plausible reduction of sensitivity and sources of imperfection from complex superconducting qubit architectures.