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… Click to show full 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.
               
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