Majorana fermions subject to the non-Abelian braid group are believed to be
the basic ingredients of future topological quantum computations. In this work,
we propose to simulate Majorana fermions of the Kitaev model in electric
circuits. We generate an arbitral number of segments in a Kitaev chain which
are in the topological phase. A pair of Majorana-like edge states emerge at the
edges of a topological sector, which is observed by impedance peaks. When the
Kitaev chain contains
N topological sectors, the degeneracy of the
zero-admittance states is
2N. A set of AC voltages along the chain plays a
role of the wave function. An \textit{LC} resonator attached to each
Majorana-like edge state registers the phase and the absolute value of the
voltage. One qubit consists of the in-phase and opposite-phase states made of
two \textit{LC} resonators installed in one topological sector. It is possible
to braid any pair of neighboring edge states with the aid of T-junction
geometry. By calculating the Berry phase acquired by their eigenfunctions, the
braiding is shown to generate one-qubit and two-qubit unitary operations. We
explicitly construct Clifford quantum gates based on them. The present scheme
may simulate topological quantum computations based on electric circuits.
We introduce a one-dimensional system of fermionic atoms in an optical lattice whose phase diagram includes topological states of different symmetry classes with a simple possibility to switch between them. The states and topological phase transitions between them can be identified by looking at their zero-energy edge modes which are Majorana fermions. We propose several universal methods of detecting the Majorana edge states, based on their genuine features: the zero-energy, localized character of the wave functions and the induced non-local fermionic correlations.