In studying Majorana fermions (MFs) in a spin ladder model, we numerically show that their qubit state can be read out by measuring fusion excitations in quenched inhomogeneous spin ladders. We construct an exactly solvable
T-junction spin ladder model that can be used to implement MF braid operations. With braiding simulated numerically as nonequilibrium quench processes, we verify that the MFs in our spin ladder model obey non-Abelian braiding statistics. Our scheme provides a promising platform to study exotic properties of MFs and a broad range of applications in topological quantum computation.
We study the Majorana fermions (MFs) in a spin ladder model. We propose and numerically show that the MFs qubit state can be read out by measuring the fusion excitation in the quenched inhomogeneous spin ladders. Moreover, we construct an exactly solvable T-junction spin ladder model, which can be used to implement braiding operations of MFs. With the braiding processes simulated numerically as non-equilibrium quench processes, we verify that the MFs in our spin ladder model obey the non-Abelian braiding statistics. Our scheme not only provides a promising platform to study the exotic properties of MFs, but also has broad range of applications in topological quantum computation.
A scheme in semiconducting quantum nanowire structure has been proposed to demonstrate the non-Abelian statistics for Majorana fermions in terms of braid group. The Majorana fermions are localized at the endpoints of semiconducting wires, which are deposited on an s -wave superconductor. The non-Abelian nature of Majorana fermion is manifested by the fact that the output of the different applied orders of two operations, constructed by the braid group elements, are different. In particular, the difference can be unambiguously imprinted on the quantum states of a superconducting flux qubit.