Topological phase transition and gate-controlled charge transfer in minimal topological-spin qubit circuit

Abstract

We propose a minimal topological-spin qubit circuit to investigate the non-Abelian rotations within the degenerate ground-state manifold, as well as the topological phase transition and charge transfer. From a quantum dot, the state of the Majorana system can be read out. Along with the splitting of the degenerate ground-state manifold of a topological qubit, a topological phase transition is observed, showing the existence of a Majorana fermion. By choosing the phase difference across the dots, the non-Abelian rotations and the required energetically degenerate state in the qubit can be achieved, which results in universal quantum computation. Moreover, on the basis of the measurement of the electron in quantum dots and topological qubit, this demonstrates that topologically protected tunnel braids between dots and MBSs are critical to non-Abelian rotations.