Impure codes exceeding the pure bounds for quantum local recovery
This work addresses limitations in quantum error correction for researchers in quantum computing, though it appears incremental as it builds on known bounds and code families.
The authors tackled the problem of quantum local recovery by constructing a family of impure CSS codes from J-affine variety codes that exceed existing bounds for pure quantum locally recoverable codes, demonstrating specific violations of these constraints.
Literature provides several bounds for quantum local recovery, which essentially consider the number of message qudits, the distance, the length, and the locality of the involved codes. We give a family of $J$-affine variety codes that result in impure CSS codes. These quantum codes exceed several of the above mentioned bounds that apply to pure quantum locally recoverable codes. We also discuss a connection between bounds on quantum local recovery and on weight-constrained stabilizer codes.