Braiding properties of Majorana Kramers Pairs

TL;DR

This paper analyzes the braiding of Kramers pairs of Majorana bound states, deriving the most general transformation on the ground state, and discusses implications for topological quantum computation.

Contribution

It provides a general form of the braiding transformation for Majorana Kramers pairs, highlighting their path dependence and limitations for quantum computing.

Findings

Braiding transformations are path dependent.

Kramers pairs cannot be used for topological quantum computation.

Conditions for path independence are discussed.

Abstract

We consider the braiding of Kramers pairs of Majorana bound states. We derive the most general transformation on the many-body ground state that is applied as the result of such a braiding process. The result is derived in the context of a simple toy model, but we will show that it has the most general form that is compatible with local and global conservation of electron parity. In accordance with earlier work the resulting transformation turns out to be path dependent, which shows that Kramers pairs of Majorana bound states cannot be used for topological quantum computation. We also discuss under which conditions the result is path independent and corresponds to two independent exchanges of pairs of Majorana bound states.