Two-block quantum code
Galois-qudit CSS code whose stabilizer generator matrices \(H_X=(A,B)\) and \(H_Z=(B^T,-A^T)\), are constructed from a pair of square commuting matrices \(A\) and \(B\).
Generalized constructions utilizing more than two blocks have also been considered .
- Quantum low-density parity-check (QLDPC) code — When matrices \(A\) and \(B\) have row and column weights bounded by \(W\), a two-block quantum code is a quantum LDPC code with stabilizer generators bounded by \(2W\).
- Lifted-product (LP) code — LP codes can be constructed using non-square matrices and taking a hypergraph product over a group algebra, while two-block quantum codes are constructed directly using square matrices.
- A. A. Kovalev and L. P. Pryadko, “Quantum Kronecker sum-product low-density parity-check codes with finite rate”, Physical Review A 88, (2013) arXiv:1212.6703 DOI
- M. Borello et al., “Dihedral Quantum Codes”, (2023) arXiv:2310.15092
- H.-K. Lin and L. P. Pryadko, “Quantum two-block group algebra codes”, (2023) arXiv:2306.16400
“Two-block quantum code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/two_block_quantum