Bravyi-Bacon-Shor (BBS) code[1]
Alternative names: 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].Cousins
- Subsystem hypergraph product (SHP) code— 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]. Subsystem hypergraph product and BBS codes have been numerically compared [2].
- Commuting-projector Hamiltonian code— Ground-state spaces of commuting-projector Hamiltonians with weight-two (two-body) terms cannot be used to suppress errors in adiabatic quantum computation [4], but this can be circumvented with excited-state subspaces [5] or ground-state subspaces of subsystem code Hamiltonians, e.g., using BBS codes [6,7].
Member of code lists
Primary Hierarchy
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
- [4]
- I. Marvian and D. A. Lidar, “Quantum Error Suppression with Commuting Hamiltonians: Two Local is Too Local”, Physical Review Letters 113, (2014) arXiv:1410.5487 DOI
- [5]
- Y. Cao, S. Liu, H. Deng, Z. Xia, X. Wu, and Y.-X. Wang, “Robust analog quantum simulators by quantum error-detecting codes”, (2024) arXiv:2412.07764
- [6]
- Z. Jiang and E. G. Rieffel, “Non-commuting two-local Hamiltonians for quantum error suppression”, Quantum Information Processing 16, (2017) arXiv:1511.01997 DOI
- [7]
- M. Marvian and D. A. Lidar, “Error Suppression for Hamiltonian-Based Quantum Computation Using Subsystem Codes”, Physical Review Letters 118, (2017) arXiv:1606.03795 DOI
Page edit log
- Victor V. Albert (2022-01-20) — most recent
- Srilekha Gandhari (2021-12-13)
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