A fermionic code related to the exceptional group e 8

Péter Lévay, Frédéric Holweck

Research output: Contribution to journalArticle


In this paper we study the Hamming-like fermionic code encoding three-qubits into 16 Majorana modes, recently introduced by Hastings. We show that although this fermionic code cannot be obtained from a single qubit stabilizer code via the usual procedure, it can be obtained from two qubit stabilizer codes via a glueing procedure combining both single and double occupancy embeddings of qubits into fermionic Fock space. This technique identifies the code subspace as a Cartan subspace of the largest exceptional group E 8. In arriving at these results we develop a general formalism for implementing this glueing procedure via the use of intertwiners between different subsectors of the Fock space realizing embedded qubits.

Original languageEnglish
Article number325301
JournalJournal of Physics A: Mathematical and Theoretical
Issue number32
Publication statusPublished - Jun 29 2018



  • embedding qubits into fermions
  • exceptional group E
  • fermionic codes
  • fermionic entanglement
  • theory of spinors

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modelling and Simulation
  • Mathematical Physics
  • Physics and Astronomy(all)

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