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Abstract: We initiate the study of Majorana fermion codes. These codes can be viewed asextensions of Kitaev-s 1D model of unpaired Majorana fermions in quantum wiresto higher spatial dimensions and interacting fermions. The purpose of Majoranafermion codes MFCs is to protect quantum information against low-weightfermionic errors, that is, operators acting on sufficiently small subsets offermionic modes. We examine to what extent MFCs can surpass qubit stabilizercodes in terms of their stability properties. A general construction of 2D MFCsis proposed which combines topological protection based on a macroscopic codedistance with protection based on fermionic parity conservation. Finally, weuse MFCs to show how to transform any qubit stabilizer code to a weaklyself-dual CSS code.

Author: Sergey Bravyi, Bernhard Leemhuis, Barbara M. Terhal


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