A fermionic code related to the exceptional group E 8
Péter Lévay, Frédéric Holweck · Journal of Physics A Mathematical and Theoretical · 2018
Abstract 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.