Fermionic code

Description

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

Child

Cousins

  • Qubit code — While the Majorana operator algebra is isomorphic to the qubit Pauli-operator algebra via the Jordan-Wigner transformation [2], codes based on the two algebras have different notions of locality and thus qualitatively different physical interpretations.
  • Bosonic code — Bosonic (fermionic) codes are associated with bosonic (fermionic) degrees of freedom.

References

[1]
S. B. Bravyi and A. Y. Kitaev, “Fermionic Quantum Computation”, Annals of Physics 298, 210 (2002). DOI; quant-ph/0003137
[2]
A. Y. Kitaev, “Unpaired Majorana fermions in quantum wires”, Physics-Uspekhi 44, 131 (2001). DOI; cond-mat/0010440
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Zoo code information

Internal code ID: fermions

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Zoo Code ID: fermions

Cite as:
“Fermionic code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/fermions
BibTeX:
@incollection{eczoo_fermions, title={Fermionic code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/fermions} }
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Permanent link:
https://errorcorrectionzoo.org/c/fermions

Cite as:

“Fermionic code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/fermions

Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/quantum/fermions/fermions.yml.