Bravyi-Bacon-Shor (BBS) code[1] 


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.


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].




  • Subsystem QPC — The BBS code construction can utilize different classical codes in different rows and columns of \(A\), while the subsystem construction does not; see [1; pg. 4]


S. Bravyi, “Subsystem codes with spatially local generators”, Physical Review A 83, (2011) arXiv:1008.1029 DOI
M. Li and T. J. Yoder, “A Numerical Study of Bravyi-Bacon-Shor and Subsystem Hypergraph Product Codes”, (2020) arXiv:2002.06257
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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.
  title={Bravyi-Bacon-Shor (BBS) code},
  booktitle={The Error Correction Zoo},
  editor={Albert, Victor V. and Faist, Philippe},
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Cite as:

“Bravyi-Bacon-Shor (BBS) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022.