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arXiv · 1801.06998

A fermionic code related to the exceptional group $E_8$

Péter Lévay·Frédéric Holweck
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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.

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Péter Lévay, Frédéric Holweck. 2018-01-22. A fermionic code related to the exceptional group $E_8$. https://doi.org/10.1088/1751-8121/aac192

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