From Interacting Majorana to Universal Topological Defects

Ising anyons, Majorana fermions (MF) and zero energy Majorana bound states (MBS) have promising prospects in topological quantum computing (TQC) because of their ability to store quantum states non-locally in space and insensitivity to local decoherence. They appear in topological phases, such as a Pfaffian quantum Hall state and a topological superconductor. There are generalizations of MBS as twist defects, also known as parafermion or fractional MBS, in Abelian topological phases with global symmetries. Unfortunately, these objects are not powerful enough to assemble a TQC that can perform universal operations using topological braiding operations alone. On the other hand, there are anyonic quasiparticles, like the Fibonacci anyon in a Read-Rezayi quantum Hall state, that are universal in the TQC sense. However, these are quantum dynamical excitations, which can be challenging to spatially manipulate and susceptible to temperature fluctuations in a thermodynamic system. We propose new universal topological defects, which are semi-classical and static, in superconducting systems of many-body interacting MFs.