Majorana surface code[1,2] 

Description

Majorana analogue of the surface code defined on a 2D 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

  • Kitaev surface code — The Majorana surface code is a Majorana stabilizer analogue of the surface code.
  • Majorana box qubit — Majorana box qubits, such as hexons, tetrons, octons, and dodecons, are placed onto patches of a 2D lattice to form Majorana surface codes [3; Table I].

References

[1]
S. Vijay, T. H. Hsieh, and L. Fu, “Majorana Fermion Surface Code for Universal Quantum Computation”, Physical Review X 5, (2015) arXiv:1504.01724 DOI
[2]
L. A. Landau et al., “Towards Realistic Implementations of a Majorana Surface Code”, Physical Review Letters 116, (2016) arXiv:1509.05345 DOI
[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_surface

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

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

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