Bicycle code[1]
Description
A CSS code whose stabilizer generator matrix blocks are \(H_{X}=H_{Z}=(A|A^T)\), where \(A\) is a circulant matrix. The fact that \(A\) commutes with its transpose ensures that the CSS condition is satisfied. Bicycle codes are the first QLDPC codes.
Parents
- Generalized homological-product qubit CSS code
- Generalized bicycle (GB) code — A GB code with whose circulants satistfy \(B = A^T\) reduces to a bicycle code.
Cousin
- Quantum LDPC (QLDPC) code — Bicycle codes are the first QLDPC codes [1].
References
- [1]
- D. J. C. MacKay, G. Mitchison, and P. L. McFadden, “Sparse-Graph Codes for Quantum Error Correction”, IEEE Transactions on Information Theory 50, 2315 (2004) arXiv:quant-ph/0304161 DOI
Page edit log
- Victor V. Albert (2024-05-09) — most recent
Cite as:
“Bicycle code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/bicycle