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].
Gates
Notes
See Ref. [5] for an introduction into Majorana-based qubits.
Parent
- Qubit code — The Majorana operator algebra is isomorphic to the qubit Pauli-operator algebra via the Jordan-Wigner transformation [6]. However, Majorana codes and the noise they are designed for are based on a different notion of locality.
Child
Cousin
- Bosonic code — Bosonic (fermionic) codes are associated with bosonic (fermionic) degrees of freedom.
References
- [1]
- S. B. Bravyi and A. Yu. Kitaev, “Fermionic Quantum Computation”, Annals of Physics 298, 210 (2002) arXiv:quant-ph/0003137 DOI
- [2]
- E. Knill, “Fermionic Linear Optics and Matchgates”, (2001) arXiv:quant-ph/0108033
- [3]
- B. M. Terhal and D. P. DiVincenzo, “Classical simulation of noninteracting-fermion quantum circuits”, Physical Review A 65, (2002) arXiv:quant-ph/0108010 DOI
- [4]
- S. Bravyi, “Lagrangian representation for fermionic linear optics”, (2004) arXiv:quant-ph/0404180
- [5]
- F. Hassler, “Majorana Qubits”, (2014) arXiv:1404.0897
- [6]
- A. Y. Kitaev, “Unpaired Majorana fermions in quantum wires”, Physics-Uspekhi 44, 131 (2001) arXiv:cond-mat/0010440 DOI
Page edit log
- Victor V. Albert (2022-12-04) — most recent
- Victor V. Albert (2021-12-01)
Cite as:
“Fermionic code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/fermions