Majorana color code

Majorana color code[1–3]

Description

Majorana analogue of the color code defined on a 2D tricolorable lattice and constructed out of Majorana box qubit codes placed on patches of the lattice.

Gates

Ordinary and twist-based lattice surgery [3] (see also [4]).

Fault Tolerance

Ordinary and twist-based lattice surgery can be made fault tolerant [3] (see also [4]).

Parent

Majorana stabilizer code

Cousins

2D color code — The Majorana color code is a Majorana stabilizer analogue of the 2D color code.
Majorana box qubit — Majorana box qubits, such as hexons, tetrons, octons, and decons, are placed onto patches of a 2D lattice to form Majorana color codes [3; Table I].
Majorana subsystem stabilizer code — The 3D subsystem color code has a Majorana variant which supports a 2D Majorana color code on its surface [5].

References

[1]: S. Bravyi, B. M. Terhal, and B. Leemhuis, “Majorana fermion codes”, New Journal of Physics 12, 083039 (2010) arXiv:1004.3791 DOI
[2]: M. B. Hastings, “Small Majorana Fermion Codes”, (2017) arXiv:1703.00612
[3]: D. Litinski and F. von Oppen, “Quantum computing with Majorana fermion codes”, Physical Review B 97, (2018) arXiv:1801.08143 DOI
[4]: C. McLauchlan and B. Béri, “A new twist on the Majorana surface code: Bosonic and fermionic defects for fault-tolerant quantum computation”, Quantum 8, 1400 (2024) arXiv:2211.11777 DOI
[5]: A. Kubica and B. Yoshida, “Ungauging quantum error-correcting codes”, (2018) arXiv:1805.01836

Page edit log

Victor V. Albert (2024-02-27) — most recent

Cite as:

“Majorana color code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/majorana_color

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/majorana/majorana_color.yml.