Topological quantum computation away from the ground state with Majorana fermions

TL;DR

This paper demonstrates that topological quantum computation with Majorana fermions can be performed away from the ground state, as long as fermion parity is conserved and Majorana interactions are absent, broadening practical implementation possibilities.

Contribution

It shows that topological protection extends to excited states in Majorana-based systems, relaxing the requirement to stay in the ground state for quantum computation.

Findings

Topological protection applies beyond the ground state.

Fermion parity conservation is key to protection.

Protection persists despite low-energy excitations.

Abstract

We relax one of the requirements for topological quantum computation with Majorana fermions. Topological quantum computation was discussed so far as manipulation of the wave function within degenerate many body ground state. The simplest particles providing degenerate ground state, Majorana fermions, often coexist with extremely low energy excitations, so keeping the system in the ground state may be hard. We show that the topological protection extends to the excited states, as long as the Majorana fermions do not interact neither directly, nor via the excited states. This protection relies on the fermion parity conservation, and so it is generic to any implementation of Majorana fermions.