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\([[47,1,11]]\) quantum QR code[1]

Description

A \([[47,1,11]]\) self-dual CSS code constructed from a binary quadratic-residue code. It is one of the shortest known qubit stabilizer codes of distance eleven that realizes the full Clifford group transversally [2].

Protection

Detects up to 10-qubit errors and corrects up to 5-qubit errors.

Transversal Gates

All logical Clifford gates are realized transversally [2].

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
Coherent-parity-check (CPC) code
Qubit CSS codeCSS Stabilizer Hamiltonian-based QECC Quantum
Parents
Qubit CSS code
Quantum quadratic-residue (QR) codeCSS Stabilizer Hamiltonian-based QECC Quantum
The \([[47,1,11]]\) code is a qubit quantum QR code [1,2].
\([[47,1,11]]\) quantum QR code

References

[1]
A. W. Cross, D. P. DiVincenzo, and B. M. Terhal, “A comparative code study for quantum fault-tolerance”, (2009) arXiv:0711.1556
[2]
S. P. Jain and V. V. Albert, “Transversal Clifford and T-Gate Codes of Short Length and High Distance”, IEEE Journal on Selected Areas in Information Theory 6, 127 (2025) arXiv:2408.12752 DOI
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Zoo Code ID: stab_47_1_11

Cite as:
“\([[47,1,11]]\) quantum QR code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/stab_47_1_11
BibTeX:
@incollection{eczoo_stab_47_1_11, title={\([[47,1,11]]\) quantum QR code}, booktitle={The Error Correction Zoo}, year={2026}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/stab_47_1_11} }
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Permanent link:
https://errorcorrectionzoo.org/c/stab_47_1_11

Cite as:

“\([[47,1,11]]\) quantum QR code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/stab_47_1_11

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/stabilizer/css/stab_47_1_11.yml.