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BB5 code[1]

Description

A BB code with weight-five stabilizer generators (contrasting with the weight-six checks of standard BB codes), designed and benchmarked for long chains of trapped ions [1].

Two highlighted instances are \([[30,4,5]]\) and \([[48,4,7]]\) [1]. Their distances exceed those of BB6 codes with the polynomial form of Ref. [2] at the same \([[n,k]]\), namely \([[30,4,4]]\) and \([[48,4,6]]\) [1]. Other BB6 codes reach \([[30,4,6]]\) [3].

Fault Tolerance

Circuit-level simulations in [1] use BP-OSD for BB5 and BB6 instances under an ion-chain noise model.For physical error rate \(10^{-3}\), the \([[48,4,7]]\) BB5 instance achieves logical error rate per syndrome round and per logical qubit \(\approx 5\times 10^{-5}\), about \(4\times\) lower than the best BB6 baseline considered in [1]. In that comparison, it also matches the logical error rate of a distance-7 surface code while using about \(4\times\) fewer physical qubits per logical qubit.

Member of code lists

Primary Hierarchy

Quantum Domain
Qubit Kingdom
Qubit codeQECC Quantum
Union stabilizer (USt) codeQECC Quantum
Qubit stabilizer codeQubit Stabilizer Hamiltonian-based QECC Quantum
Coherent-parity-check (CPC) code
Qubit CSS codeCSS Stabilizer Hamiltonian-based QECC Quantum
Generalized homological-product qubit CSS codeQLDPC Qubit CSS Generalized homological-product Stabilizer Hamiltonian-based QECC Quantum
Bivariate bicycle (BB) codeQLDPC Qubit CSS Generalized homological-product Lattice stabilizer Stabilizer Hamiltonian-based QECC Quantum
Parents
Bivariate bicycle (BB) code
BB5 code

References

[1]
M. Ye and N. Delfosse, “Quantum error correction for long chains of trapped ions”, Quantum 9, 1920 (2025) arXiv:2503.22071 DOI
[2]
S. Bravyi, A. W. Cross, J. M. Gambetta, D. Maslov, P. Rall, and T. J. Yoder, “High-threshold and low-overhead fault-tolerant quantum memory”, Nature 627, 778 (2024) arXiv:2308.07915 DOI
[3]
M. Wang and F. Mueller, “Coprime Bivariate Bicycle Codes and Their Layouts on Cold Atoms”, Quantum 10, 2009 (2026) arXiv:2408.10001 DOI
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Zoo Code ID: bb5

Cite as:
“BB5 code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/bb5, arXiv:2606.11484
BibTeX:
@incollection{eczoo_bb5,
title={BB5 code},
booktitle={The Error Correction Zoo},
year={2026},
editor={Albert, Victor V. and Faist, Philippe},
eprint={2606.11484},
doi={10.48550/arXiv.2606.11484},
url={https://errorcorrectionzoo.org/c/bb5}
}
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Permanent link:
https://errorcorrectionzoo.org/c/bb5

Cite as:

“BB5 code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/bb5, arXiv:2606.11484

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/stabilizer/qldpc/balanced_product/lp/bb/bb5.yml.