Welcome to the Fermionic Kingdom.

Fermionic code Finite-dimensional quantum error-correcting code encoding a logical Hilbert space into a physical Fock space of fermionic modes. Codes are typically described using Majorana operators, which are linear combinations of fermionic creation and annihilation operators [1]. Parent of: Majorana stabilizer code. Cousins: Qubit code, Bosonic code.
Majorana fermion stabilizer codes are stabilizer codes whose stabilizers are products of an even number of Majorana fermion operators, analogous to Pauli strings for a traditional stabilizer code and referred to as Majorana stabilizers. The codespace is the mutual $$+1$$ eigenspace of all Majorana stabilizers. In such systems, Majorana fermions may either be considered individually or paired into creation and annihilation operators for fermionic modes. Codes can be denoted as $$[[n,k,d]]_{f}$$ [3], where $$n$$ is the number of fermionic modes. Protection: Detects products of Majorana operators with weight up to $$d-1$$. Physically, protects against dephasing errors caused by coupling of fermion density to the environment and bit-flip errors caused by quasiparticle poisoning processes. Parents: Fermionic code, Qubit stabilizer code.

## References

[1]
S. B. Bravyi and A. Y. Kitaev, “Fermionic Quantum Computation”, Annals of Physics 298, 210 (2002). DOI; quant-ph/0003137
[2]
S. Bravyi, B. M. Terhal, and B. Leemhuis, “Majorana fermion codes”, New Journal of Physics 12, 083039 (2010). DOI; 1004.3791
[3]
Sagar Vijay and Liang Fu, “Quantum Error Correction for Complex and Majorana Fermion Qubits”. 1703.00459