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We study the Majorana fermions (MFs) in a spin ladder model. We propose andnumerically show that the MFs qubit state can be read out by measuring thefusion excitation in the quenched inhomogeneous spin ladders. Moreover, weconstruct an exactly solvable T-junction spin ladder model, which can be usedto implement braiding operations of MFs. With the braiding processes simulatednumerically as non-equilibrium quench processes, we verify that the MFs in ourspin ladder model obey the non-Abelian braiding statistics. Our scheme not onlyprovides a promising platform to study the exotic properties of MFs, but alsohas broad range of applications in topological quantum computation.

Measuring Majorana fermions qubit state and non-Abelian braiding statistics in quenched inhomogeneous spin ladders