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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 \([[48,4,7]]\), which improve the best-known BB6 distances at the same \([[n,k]]\): respectively \([[30,4,4]]\) and \([[48,4,6]]\) [1].

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 codeStabilizer Hamiltonian-based Qubit QECC Quantum
Coherent-parity-check (CPC) code
Qubit CSS codeCSS Stabilizer Hamiltonian-based QECC Quantum
Generalized homological-product qubit CSS codeGeneralized homological-product QLDPC CSS Stabilizer Hamiltonian-based QECC Quantum
Bivariate bicycle (BB) codeGeneralized homological-product Lattice stabilizer QLDPC CSS 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
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Zoo Code ID: bb5

Cite as:
“BB5 code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2025. https://errorcorrectionzoo.org/c/bb5
BibTeX:
@incollection{eczoo_bb5, title={BB5 code}, booktitle={The Error Correction Zoo}, year={2025}, editor={Albert, Victor V. and Faist, Philippe}, 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.), 2025. https://errorcorrectionzoo.org/c/bb5

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