Small Majorana Fermion Codes
arXiv:1703.00612
Abstract
We consider Majorana fermion stabilizer codes with small number of modes and distance. We give an upper bound on the number of logical qubits for distance codes, and we construct Majorana fermion codes similar to the classical Hamming code that saturate this bound. We perform numerical studies and find other distance and codes that we conjecture have the largest possible number of logical qubits for the given number of physical Majorana modes. Some of these codes have more logical qubits than any Majorana fermion code derived from a qubit stabilizer code.
11 pages, 1 figure