Majorana color code[13] 

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

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].

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”, (2023) arXiv:2211.11777
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Zoo Code ID: majorana_color

Cite as:
“Majorana color code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/majorana_color
BibTeX:
@incollection{eczoo_majorana_color, title={Majorana color code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/majorana_color} }
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“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.