# Scalable Fermionic Error Correction in Majorana Surface Codes

## TL;DR

This paper investigates the error correction capabilities of Majorana Surface Codes, demonstrating their robustness against fermionic errors and establishing error thresholds that surpass traditional spin-based topological codes, making them promising for quantum memory.

## Contribution

The study introduces error thresholds for Majorana Surface Codes under fermionic errors and develops new lattice gauge theories to model measurement errors, highlighting their potential for robust quantum memory.

## Key findings

- Error threshold of ~11% for quasiparticle poisoning errors.
- Error threshold of ~16% when fermionic bilinear errors dominate.
- Higher error thresholds compared to spin-based topological codes.

## Abstract

We study the error correcting properties of Majorana Surface Codes (MSC), topological quantum codes constructed out of interacting Majorana fermions, which can be used to store quantum information and perform quantum computation. These quantum memories suffer from purely "fermionic" errors, such as quasiparticle poisoning (QP), that have no analog in conventional platforms with bosonic qubits. In physical realizations where QP dominates, we show that errors can be corrected provided that the poisoning rate is below a threshold of $\sim11\%$. When QP is highly suppressed and fermionic bilinear ("bosonic") errors become dominant, we find an error threshold of $\sim16\%$, which is much higher than the threshold for spin-based topological memories like the Surface code or the Color code. In addition, we derive new lattice gauge theories to account for measurement errors. These results, together with the inherent error suppression provided by the superconducting gap in physical realizations of the MSC, makes this a strong candidate for a robust topological quantum memory.