Synthetic Topological Degeneracy by Anyon Condensation

TL;DR

This paper introduces a novel form of topological degeneracy caused by anyon condensation along lines in 2D topological states, with potential applications in quantum memory and fault-tolerant quantum computing.

Contribution

It presents a new type of topological degeneracy from line-defect anyon condensation, generalizing Majorana zero-modes and enabling topological quantum computation.

Findings

Line-defects induce topological degeneracy at their ends.

Ends of line-defects exhibit projective non-Abelian statistics.

Potential for fault-tolerant quantum memory and computation.

Abstract

Topological degeneracy is the degeneracy of the ground states in a many-body system in the large-system-size limit. Topological degeneracy cannot be lifted by any local perturbation of the Hamiltonian. The topological degeneracies on closed manifolds have been used to discover/define topological order in many-body systems, which contain excitations with fractional statistics. In this paper, we study a new type of topological degeneracy induced by condensing anyons along a line in 2D topological ordered states. Such topological degeneracy can be viewed as carried by each end of the line-defect, which is a generalization of Majorana zero-modes. The topological degeneracy can be used as a quantum memory. The ends of line-defects carry projective non-Abelian statistics, and braiding them allow us to perform fault tolerant quantum computations.