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Majorana fermions subject to the non-Abelian braid group are believed to bethe basic ingredients of future topological quantum computations. In this work,we propose to simulate Majorana fermions of the Kitaev model in electriccircuits based on the observation that the circuit Laplacian can be madeidentical to the Hamiltonian. A set of AC voltages along the chain plays a roleof the wave function. We generate an arbitrary number of topological segmentsin a Kitaev chain. A pair of topological edge states emerge at the edges of atopological segment. Its wave function is observable by the position and thephase of a peak in impedance measurement. It is possible to braid any pair ofneighboring edge states with the aid of T-junction geometry. By calculating theBerry phase acquired by their eigenfunctions, the braiding is shown to generateone-qubit and two-qubit unitary operations. We explicitly construct Cliffordquantum gates based on them. We also present an operator formalism by regardinga topological edge state as a topological soliton intertwining the trivialsegment and the topological segment. Our analysis shows that theelectric-circuit approach can simulate the Majorana-fermion approach totopological quantum computations.

Non-Abelian braiding of Majorana-like edge states and topological quantum computations in electric circuits