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\([[13,1,5]]\) quantum QR code[1; pg. 11]

Description

Thirteen-qubit cyclic Hermitian qubit code derived from a quaternary quadratic-residue code using the Hermitian construction [2][1; pg. 11]. The code admits a check matrix whose rows are cyclic permutations of the Pauli string \(XXZZIZIIIZIZZ\).

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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
Hermitian qubit codeStabilizer Hamiltonian-based QECC Quantum
Parents
Hermitian qubit code
Quantum quadratic-residue (QR) codeCSS Stabilizer Hamiltonian-based QECC Quantum
Small-distance qubit stabilizer codeStabilizer Hamiltonian-based Qubit Small-distance block quantum QECC Quantum
\([[13,1,5]]\) quantum QR code

References

[1]
F. Vatan, V. P. Roychowdhury, and M. P. Anantram, “Spatially Correlated Qubit Errors and Burst-Correcting Quantum Codes”, (1997) arXiv:quant-ph/9704019
[2]
R. Dastbasteh and P. Lisonek, “New quantum codes from self-dual codes over F_4”, (2022) arXiv:2211.00891
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Zoo Code ID: quad_residue_13_1_5

Cite as:
“\([[13,1,5]]\) quantum QR code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/quad_residue_13_1_5
BibTeX:
@incollection{eczoo_quad_residue_13_1_5, title={\([[13,1,5]]\) quantum QR code}, booktitle={The Error Correction Zoo}, year={2026}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/quad_residue_13_1_5} }
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Permanent link:
https://errorcorrectionzoo.org/c/quad_residue_13_1_5

Cite as:

“\([[13,1,5]]\) quantum QR code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/quad_residue_13_1_5

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/small_distance/small/13/quad_residue_13_1_5.yml.