Minimal setup for non-Abelian braiding of Majorana zero modes

Abstract

Braiding Majorana zero modes (MZMs) is the key procedure toward topological quantum computation. However, the complexity of the braiding manipulation hinders its experimental realization.Here we propose an experimental setup composing of MZMs and a quantum dot state which can substantially simplify the braiding protocol of MZMs. Such braiding scheme, which corresponds to a specific closed loop in the parameter space, is quite universal and can be realized in various platforms. Moreover, the braiding results can be directly measured and manifested through electric current, which provides a simple and novel way to detect the non-Abelian statistics of MZMs.

Unveiling non-Abelian statistics of vortex Majorana bound states in iron-based superconductors using fermionic modes

“…Finally, using a single fermionic mode, we propose a portable protocol to perform the braiding operations over vMBSs. The braiding completeness is closely related to the geometric phase of Majorana modes accumulated during the braiding process [55]. Our proposals shed light on scalable TQC in FeSCs.…”

“…Since only a single fermionic mode is required, our protocol brings experimental convenience in FeSCs platforms by driving a single quantum-dot structure with an AFM/STM tip to approach the two vortices alternately. Besides, since the braiding process induces a local charge transfer between vortices which is closely related to the braiding completeness [55], the braiding outcome may be readout by performing local charge sensing measurements through the AFM/STM tip [66][67][68]81].…”

“…The transition probability | φ + AB (0)|φ − AB (T s ) | 2 (or | φ + CD (0)|φ − CD (T s ) | 2 ) signals the braiding completeness for our protocol. This quantity is directly related to the solid angleΩ c = arccos(E d / E 2 d + t 2 c) (which is also the geometric phase of γ A and γ C accumulated during the operation) enclosed by the trajectory of γ 2 in the space (γ 2 , γ A , γ C ) through the relation| φ + CD (0)|φ − CD (T s ) | = 1−cos(2Ω c )[55]. Numerical simulations of our braiding protocol with two pairs of vortices (see details in the Supplementary material) demonstrates that the vMBSs qubit successfully flips from |φ − AB to |φ + AB [Fig.4…”