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.
We demonstrate a transmon-qubit readout based on the nonlinear response to a drive of polaritonic meters in situ coupled to the qubit. Inside a three-dimensional readout cavity, we place a transmon molecule consisting of a transmon qubit and an ancilla mode interacting via nonperturbative cross-Kerr-coupling. The cavity couples strongly only to the ancilla mode, leading to hybridized lower and upper polaritonic meters. Both polaritons are anharmonic and dissipative, as they inherit a self-Kerr nonlinearity
U from the ancilla and effective decay $\ensuremath{\kappa}$ from the open cavity. Via the ancilla, the polariton meters also inherit the nonperturbative cross-Kerr-coupling to the qubit. This results in a high qubit-dependent displacement $2\ensuremath{\chi}>\ensuremath{\kappa},U$ that can be read out via the cavity without causing Purcell decay. Moreover, the polariton meters, being nonlinear resonators, present bistability, and bifurcation behavior when the probing power increases. In this work, we focus on the bifurcation at low power in the few-photon regime, called the mesoscopic regime, which is accessible when the self-Kerr and decay rates of the polariton meter are similar, $U\ensuremath{\sim}\ensuremath{\kappa}$. Capitalizing on a latching mechanism by bifurcation, the readout is sensitive to transmon-qubit relaxation error only in the first tens of nanoseconds. We thus report a single-shot fidelity of 98.6% while having an integration time of 500 ns and no requirement for an external quantum-limited amplifier.