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

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

Description

A \([[54,6,5]]\) qubit stabilizer code defined whose encoder-respecting form is the graph of a five-cover of the icosahedron [1].

Cousin

Icosahedron code— The encoder-respecting form of the \([[54,6,5]]\) five-covered icosahedral code is the graph of a five-cover of the icosahedron [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

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”, (2024) arXiv:2411.14448

Page edit log

Victor V. Albert (2024-12-13) — most recent

Cite as:

“\([[54,6,5]]\) five-covered icosahedral code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/quantum_icosahedron

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