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Qudit GNU PI code[1]

Description

Extension of the GNU PI codes to those encoding logical qudits into physical qubits. Codewords can be expressed as superpositions of Dicke states with coefficients are square-roots of polynomial coefficients, with the case of binomial coefficients reducing to the GNU PI codes.

Member of code lists

Primary Hierarchy

Quantum Domain
Qubit Kingdom
Qubit codeQECC Quantum
PI qubit codePI Cyclic quantum QECC Quantum
Parents
PI qubit code
Amplitude-damping (AD) codeQECC AQECC Quantum
Qudit GNU PI codes protect against AD errors.
Qudit GNU PI code
Children
GNU PI code
Qudit GNU codes encoding logical qubits reduce to GNU codes.

References

[1]
Y. Ouyang, “Permutation-invariant qudit codes from polynomials”, Linear Algebra and its Applications 532, 43 (2017) arXiv:1604.07925 DOI
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Zoo Code ID: qudit_gnu_permutation_invariant

Cite as:
“Qudit GNU PI code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/qudit_gnu_permutation_invariant
BibTeX:
@incollection{eczoo_qudit_gnu_permutation_invariant, title={Qudit GNU PI code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/qudit_gnu_permutation_invariant} }
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Permanent link:
https://errorcorrectionzoo.org/c/qudit_gnu_permutation_invariant

Cite as:

“Qudit GNU PI code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/qudit_gnu_permutation_invariant

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/permutation_invariant/gnu/qudit_gnu_permutation_invariant.yml.