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Majorana loop stabilizer code (MLSC)[1]

Description

A single-error-correcting fermion-into-qubit encoding defined on a 2D qubit lattice whose stabilizers are associated with loops in the lattice.

Protection

The code can correct single-qubit errors [1].

Member of code lists

Primary Hierarchy

Quantum Domain
Qubit Kingdom
Qubit codeQECC Quantum
Union stabilizer (USt) codeQECC Quantum
Qubit stabilizer codeStabilizer Hamiltonian-based Qubit QECC Quantum
Fermion-into-qubit code
Bosonization codeQLDPC Lattice stabilizer Stabilizer Hamiltonian-based Qubit QECC Quantum
2D bosonization codeLattice stabilizer Stabilizer Hamiltonian-based QECC Quantum
Parents
2D bosonization code
The MLSC on a square lattice can be obtained from exact 2D bosonization by finite-depth generalized local unitaries [2].
Majorana loop stabilizer code (MLSC)
Children
Bravyi-Kitaev superfast (BKSF) code
The BKSF code can be thought of as a particular MLSC [1].

References

[1]
Z. Jiang, J. McClean, R. Babbush, and H. Neven, “Majorana Loop Stabilizer Codes for Error Mitigation in Fermionic Quantum Simulations”, Physical Review Applied 12, (2019) arXiv:1812.08190 DOI
[2]
Y.-A. Chen and Y. Xu, “Equivalence between Fermion-to-Qubit Mappings in two Spatial Dimensions”, PRX Quantum 4, (2023) arXiv:2201.05153 DOI
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Zoo Code ID: mlsc

Cite as:
“Majorana loop stabilizer code (MLSC)”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/mlsc, arXiv:2606.11484
BibTeX:
@incollection{eczoo_mlsc,
title={Majorana loop stabilizer code (MLSC)},
booktitle={The Error Correction Zoo},
year={2026},
editor={Albert, Victor V. and Faist, Philippe},
eprint={2606.11484},
doi={10.48550/arXiv.2606.11484},
url={https://errorcorrectionzoo.org/c/mlsc}
}
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Permanent link:
https://errorcorrectionzoo.org/c/mlsc

Cite as:

“Majorana loop stabilizer code (MLSC)”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/mlsc, arXiv:2606.11484

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/stabilizer/fermion_into_qubit/bosonization/2d/mlsc.yml.