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\([[54,6,5]]\) five-covered icosahedral code[1]

Description

A \([[54,6,5]]\) qubit stabilizer code whose encoder-respecting form is the graph of a five-cover of the icosahedron [1]. The covering-space construction avoids the weight-three logical operators that occur for the bare icosahedral graph [1].

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Primary Hierarchy

Quantum Domain
Qubit Kingdom
Qubit codeQECC Quantum
Union stabilizer (USt) codeQECC Quantum
Qubit stabilizer codeStabilizer Hamiltonian-based Qubit QECC Quantum
Small-distance qubit stabilizer codeSmall-distance block quantum QECC Quantum
Parents
Small-distance qubit stabilizer code
\([[54,6,5]]\) five-covered icosahedral code

References

[1]
A. B. Khesin, J. Z. Lu, and P. W. Shor, “Universal Graph Representation of Stabilizer Codes”, PRX Quantum 6, (2025) arXiv:2411.14448 DOI
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Zoo Code ID: quantum_icosahedron

Cite as:
“\([[54,6,5]]\) five-covered icosahedral code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/quantum_icosahedron, arXiv:2606.11484
BibTeX:
@incollection{eczoo_quantum_icosahedron,
title={\([[54,6,5]]\) five-covered icosahedral code},
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/quantum_icosahedron}
}
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Permanent link:
https://errorcorrectionzoo.org/c/quantum_icosahedron

Cite as:

“\([[54,6,5]]\) five-covered icosahedral code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/quantum_icosahedron, arXiv:2606.11484

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/small_distance/quantum_icosahedron.yml.