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arXiv:2304.04270 · Physical review. B./Physical review. B

Dynamics simulation of braiding two Majorana zero modes via a quantum dot

Luting Xu, Jing Bai, Wei Feng, Xin-Qi Li

Published Sep 7, 2023• 9 citations
arXivHTMLPDF

Abstract

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 one-dimensional realization. We reveal the strong nonadiabatic effect when the dot energy level approaches zero in order to achieve a geometric phase $\ensuremath{\pi}/4$ which is required for a full exchange between the MZMs. Rather than the strategies of nonuniformly manipulating the system according to adiabatic conditions and shortcuts to adiabaticity, we propose and illustrate a more feasible scheme to suppress the nonadiabatic transition, which allows for a full exchange between the Majorana modes.

DOI
10.1103/physrevb.108.115411

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Bulletin of the American Physical Society•Jan 1, 2021•0 citations
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 one-dimensional realization. We reveal the strong nonadiabatic effect when the dot energy level approaches zero in order to achieve a geometric phase \ensuremathπ/4\ensuremath{\pi}/4\ensuremathπ/4 which is required for a full exchange between the MZMs. Rather than the strategies of nonuniformly manipulating the system according to adiabatic conditions and shortcuts to adiabaticity, we propose and illustrate a more feasible scheme to suppress the nonadiabatic transition, which allows for a full exchange between the Majorana modes.
The realization and manipulation of Majorana zero modes have drawn significant attention for their crucial role in enabling topological quantum computation. Conventional approaches to the braiding of Majorana zero modes rely on adiabatic processes. In this work, using a composite 2-Kitaev-chain system accommodating Majorana zero modes as a working example, we propose a nonadiabatic and non-Abelian geometry phase-based protocol to execute operations on these Majorana zero modes. This is possible by locally coupling the edge sites of both quantum chains with an embedded lattice defect, successfully simulating the braiding operation of two Majorana modes in a highly nonadiabatic fashion. To further enhance the robustness against control imperfections, we apply a multiple-pulse composite strategy to our quantum chain setting for second-order protection of the braiding operations. Our proposal can also support the fast and robust realization of the $\ensuremath{\pi}/8$ gate, an essential ingredient for universal quantum computation. This work hence offers a potential pathway toward the nonadiabatic and fault-tolerant control of Majorana zero modes.
Abstract Recent advances in quantum dot platforms have opened a new platform for realizing Majorana zero modes (MZMs) and simulating topological quantum computation. Here we propose an experimentally feasible setup for implementing topological X\sqrt{X}X​ X - and X -quantum gates in an interacting Y -shaped quantum-dot array. The proposed architecture enables both braiding and charge readout through simple fusion operations controlled by gate-tunable potentials. Using many-body time-dependent exact diagonalization, we analyze MZM braiding and fusion dynamics in the presence of nearest-neighbor Coulomb interactions, hopping-pairing mismatch, onsite charge fluctuations, and pairing disorder. We compute diabatic errors, braiding fidelity, and the time- and space-resolved electron and hole components of the local density of states to monitor the braiding process. Our results show that even weak interactions or pairing disorder induce oscillations in the braiding fidelity, thereby setting an upper bound on the braiding speed. Furthermore, we demonstrate that comparing fusion outcomes before and after double braiding provides a direct and experimentally accessible signature of the non-Abelian nature of MZMs in quantum-dot systems.
Majorana zero modes, characterized by non-Abelian exchange statistics, have been widely viewed as prime candidates for implementing topological quantum computing. The associated braiding and fusion operations realize topologically protected quantum gates and qubit measurements, thus providing a feasible pathway toward intrinsically fault-tolerant quantum computation. However, the experimental realization of controllable braiding and fusion of Majorana zero modes remains one of the most formidable challenges in the field.In this paper, building upon recent theoretical advances in quantum-dot-assisted schemes for realizing the braiding and fusion of Majorana zero modes, we provide a systematic introduction to the underlying theoretical foundations and detailed operational procedures, and further elucidate the experimental feasibility of the approach.Furthermore, this paper presents two lines of investigation developed within the proposed framework. Firstly, based on the quantum-dot-assisted braiding scheme, the dynamical evolution of Andreev bound states in Majorana nanowires is revealed. Secondly, employing the quantum-dot-assisted fusion scheme, numerical simulations of charge transfer along different fusion paths clarify the nontrivial fusion rules of Majorana zero modes and the corresponding operational procedures.
Abstract We propose and simulate a near-adiabatically coupling probing scheme for nontrivial fusion of a pair of Majorana zero modes (MZMs). The scheme can avoid the complexity of oscillating charge occupation in the probing quantum dot, making thus practical measurements more feasible. We also show how to extract the information of nonadiabatic transition and fermion parity violation caused during moving the MZMs together to fuse, from the initial states prepared with definite fermion parity. All the simulations, including the effective coupling between the fusing MZMs, and their coupling to the probing quantum dot, are based on the lattice model of a Rashba quantum wire in proximity contact with an s -wave superconductor, under the modulation of mini-gate voltage control.
The topic of Majorana zero modes has been a focal point of the condensed matter physicscommunity in recent times due in part to their potential applications in quantum computation.Most notably, the exotic exchange statistics of Majorana zero modes form the basis oftopologically protected quantum gates. The physical exchange, or braiding, of Majorana zeromodes is often modeled in two-dimensional systems or by using networks of wires. Recentwork has established that Majorana zero modes can be braided in a purely one-dimensionalsetting with a periodic, or Floquet, drive. Specifically, the work of Bauer et al. in Ref.[1] demonstrates that a working braiding protocol can be simulated on a Kitaev chain withperiodically modulated parameters. This Floquet system gives rise to both Majorana zeromodes and Majorana pi modes, the latter of which serves as an additional degree of freedomin the braiding protocol.We reproduce the results of Ref. [1] through numerical simulation and extend theirbraiding protocol such that it includes both disorder and interactions. We demonstrate thatthe protocol remains successful when the disorder is weak compared to the parameters of thesystem. In the case of strong disorder, we demonstrate that the protocol fails. In addition,we show that the protocol is quite sensitive to the presence of interactions. We illustratethat interactions cause a severe delocalization of the Majorana zero modes leading to thefailure of the protocol