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In this work we perform real time simulations for the dynamics of braiding a pair of Majorana zero modes (MZMs) through a quantum dot in a minimal setup of pure 1D realization. We reveal the strong nonadiabatic effect when the dot energy level approaches to zero in order to achieve a geometric phase $\pi/4$ which is required for a full exchange between the MZMs. Rather than the strategies of nonuniformly manipulating the system according to adiabatic condition and shortcuts-to-adiabaticity, we propose and illustrate a more feasible scheme to suppress the nonadiabatic transition, meanwhile which allows for a full exchange between the Majorana modes., Comment: 6 pages, 5 figures

We propose a transport probe scheme to detect the nonadiabatic transition caused by Majornana moving, which is relevant to the braiding operations in topological quantum computation. The scheme is largely based on a time dependent single-electron-wavefunction approach to quantum transport. Applying the Kitaev model, we simulate the time dependent Andreev-reflection current and examine the feasibility of using the current to infer the nonadiabatic transition. We design a scheme to determine the Landau-Zener tunneling ratio in the context of transport, and compare it with the result obtained from the isolated quantum wire. Desirable agreements are demonstrated for the proposed scheme., 8 pages, 6 figures

The nonlocal nature of the Majorana zero modes implies an inherent teleportation channel and unique transport signatures for Majorana identification. In this work we make an effort to eliminate some inconsistencies between the Bogoliubov-de Gennes equation based treatment and the method using the associated regular fermion number states of vacancy and occupation within the `second quantization' framework. We first consider a rather simple `quantum dot--Majorana wire--quantum dot' system, then a more experimentally relevant setup by replacing the quantum dots with transport leads. For the latter setup, based on the dynamical evolution of electron-hole excitations, we develop a single-particle-wavefunction approach to quantum transport, which renders both the conventional quantum scattering theory and the steady-state nonequilibrium Green's function formalism as its stationary limit. Further, we revisit the issue of Majorana tunneling spectroscopy and consider in particular the two-lead coupling setup. We present comprehensive discussions with detailed comparisons, and predict a zero-bias-limit conductance of $e^2/h$ (for symmetric coupling to the leads),which is a half of the popular result of the zero-bias-peak, or, the so-called Majorana quantized conductance ($2e^2/h$). The present work may arouse a need to reexamine some existing studies and the proposed treatment is expected to be involved in analyzing future experiments in this fast developing field., 12 pages, 4 figures

In solid-state circuit QED system, we extend the previous study of generating and stabilizing two-qubit Bell state [Phys. Rev. A 82, 032335 (2010)], to three-qubit GHZ state. In dispersive regime, we employ the homodyne joint readout for multiple qubits to infer the state for further processing, and in particular use it to stabilize the state directly by means of an alternate-flip-interrupted Zeno (AFIZ) scheme. Moreover, the state-of-the-art feedback action based on the filtered current enables not only a deterministic generation of the pre-GHZ state in the initial stage, but also a fast recovery from the environment-caused degradation in the later stabilization process. We show that the proposed scheme can maintain the state with high fidelity if the efficient quantum measurement and rapid single-qubit rotations are available., 6 pages, 5 figures