A fermionic code related to the exceptional group $E_8$

Abstract

In this paper we study the Hamming-like fermionic code encoding three-qubits into sixteen 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 however, it can be obtained from two, qubit stabilizer ones 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.

14 pages

References in corpus (2)

• Hidden Variables and the Two Theorems of John Bell
• Embedding qubits into fermionic Fock space, peculiarities of the four-qubit case

Cited by in corpus (1)

• Identifiability and singular locus of secant varieties to spinor varieties