Majorana fermion codes

Sergey Bravyi, Bernhard Leemhuis, B.M. Terhal

Research output: Contribution to journalArticleScientificpeer-review

63 Citations (Scopus)


We initiate the study of Majorana fermion codes (MFCs). These codes can be viewed as extensions of Kitaev's one-dimensional (ID) model of unpaired Majorana fermions in quantum wires to higher spatial dimensions and interacting fermions. The purpose of MFCs is to protect quantum information against low-weight fermionic errors, that is, operators acting on sufficiently small subsets of fermionic modes. We examine to what extent MFCs can surpass qubit stabilizer codes in terms of their stability properties. A general construction of 2D MFCs is proposed that combines topological protection based on a macroscopic code distance with protection based on fermionic parity conservation. Finally, we use MFCs to show how to transform any qubit stabilizer code to a weakly self-dual CSS code.

Original languageEnglish
Article number083039
Number of pages21
JournalNew Journal of Physics
Publication statusPublished - 2010
Externally publishedYes


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