Scalable Fermionic Error Correction in 2D Majorana Surface Codes

The Majorana Surface Code (MSC) is a topological quantum code constructed out of interact-
ing Majorana fermions, which can be used to store quantum information and perform topological
quantum computation. In this talk, we show how purely fermionic errors (quasiparticle poisoning
events) can be corrected provided the error rate is below a certain threshold. In addition, we show
how bosonic and measurement errors poses higher error thresholds than spin-based topological memories like the Surface Code and the Color Code. These results together with the inherent protection against thermal fluctuations given by the
superconducting gap make the MSC a strong candidate for a robust topological quantum memory.