Bravyi-Bacon-Shor (BBS) code[1] 

Also known as Generalized Bacon-Shor code.

Description

An \([[n,k,d]]\) CSS subsystem stabilizer code generalizing Bacon-Shor codes to a larger set of qubit geometries. Defined through a binary matrix \(A\) such that physical qubits live on sites \((i,j)\) whenever \(A_{i,j}=1\). The gauge group is generated by 2-qubit operators, including \(XX\) interations between any two qubits sharing a column in \(A\), and \(ZZ\) interations between two qubits sharing a row. The code parameters are: \(n=\sum_{i,j}A_{i,j}\), \(k=\text{rank}(A)\), and the distance is the minimum weight of any row or column.

Protection

Detects errors on \(d-1\) qubits, corrects errors on \(\left\lfloor (d-1)/2 \right\rfloor\) qubits, where \(d\) is the minimum weight of a row or column in \(A\) [2].

Rate

A class of BBS codes [3] saturate the subsystem bound \(kd = O(n)\) [1].

Parent

Child

Cousins

References

[1]
S. Bravyi, “Subsystem codes with spatially local generators”, Physical Review A 83, (2011) arXiv:1008.1029 DOI
[2]
M. Li and T. J. Yoder, “A Numerical Study of Bravyi-Bacon-Shor and Subsystem Hypergraph Product Codes”, (2020) arXiv:2002.06257
[3]
T. J. Yoder, “Optimal quantum subsystem codes in two dimensions”, Physical Review A 99, (2019) arXiv:1901.06319 DOI
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Zoo Code ID: bravyi_bacon_shor

Cite as:
“Bravyi-Bacon-Shor (BBS) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/bravyi_bacon_shor
BibTeX:
@incollection{eczoo_bravyi_bacon_shor, title={Bravyi-Bacon-Shor (BBS) code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/bravyi_bacon_shor} }
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Permanent link:
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Cite as:

“Bravyi-Bacon-Shor (BBS) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/bravyi_bacon_shor

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/subsystem/qldpc/bravyi_bacon_shor.yml.