Braiding errors in interacting Majorana quantum wires

Braiding With Majorana Fermions

This paper is an introduction to relationships between topology, quantum computing and the properties of fermions. In particular we study the remarkable unitary braid group representations associated with Majorana fermions.

Majorana Braiding with Thermal Noise.

We investigate the self-correcting properties of a network of Majorana wires, in the form of a trijunction, in contact with a parity-preserving thermal environment. As opposed to the case where Majorana bound states are immobile, braiding Majorana bound states within a trijunction introduces dangerous error processes that we identify. Such errors prevent the lifetime of the memory from increasi...

Interplay of disorder and interaction in Majorana quantum wires.

We study the interplay between disorder and interaction in one-dimensional topological superconductors which carry localized Majorana zero-energy states. Using Abelian bosonization and the perturbative renormalization group approach, we obtain the renormalization group flow and the associated scaling dimensions of the parameters and identify the critical points of the low-energy theory. We pred...

Helical liquids and Majorana bound states in quantum wires.

We show that the combination of spin-orbit coupling with a Zeeman field or strong interactions may lead to the formation of a helical electron liquid in single-channel quantum wires, with spin and velocity perfectly correlated. We argue that zero-energy Majorana bound states are formed in various situations when such wires are situated in proximity to a conventional s-wave superconductor. This ...

Majorana Fermions in Equilibrium and Driven Cold Atom Quantum Wires