Quantifying robustness and locality of Majorana bound states in interacting systems

TL;DR

This paper rigorously analyzes how Majorana bound states in interacting systems can be characterized by their locality, which influences their robustness and potential for fault-tolerant quantum computing.

Contribution

It introduces a method to define Majorana bound states in many-body ground states and links their locality to their protection and braiding capabilities in interacting systems.

Findings

Locality constrains MBS coupling to environment

Quantifies energy degeneracy protection

Assesses feasibility of non-abelian braiding

Abstract

Protecting qubits from perturbations is a central challenge in quantum computing. Topological superconductors with separated Majorana bound states (MBSs) provide a strong form of protection that only depends on the locality of perturbations. While the link between MBS separation, robust degeneracy, and protected braiding is well understood in non-interacting systems, recent experimental progress in short quantum-dot-based Kitaev chains highlights the need to establish these connections rigorously for interacting systems. We do this by defining MBSs from many-body ground states and show how their locality constrains their coupling to an environment. This, in turn, quantifies the protection of the energy degeneracy and the feasibility of non-abelian braiding.