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\([[16,4,3]]\) dodecahedral code[1]

Description

A \([[16,4,3]]\) qubit stabilizer code defined whose encoder-respecting form is the graph of vertices of a dodecahedron [1].

Rate

The code has a rate of \(1/4\), higher than that of the five-qubit perfect code.

Encoding

Low-depth encoding circuit [1].

Cousin

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
\([[16,4,3]]\) dodecahedral code

References

[1]
A. B. Khesin, J. Z. Lu, and P. W. Shor, “Universal graph representation of stabilizer codes”, (2024) arXiv:2411.14448
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Zoo Code ID: quantum_dodecahedron

Cite as:
“\([[16,4,3]]\) dodecahedral code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/quantum_dodecahedron
BibTeX:
@incollection{eczoo_quantum_dodecahedron, title={\([[16,4,3]]\) dodecahedral code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/quantum_dodecahedron} }
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Permanent link:
https://errorcorrectionzoo.org/c/quantum_dodecahedron

Cite as:

“\([[16,4,3]]\) dodecahedral code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/quantum_dodecahedron

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