Problem
Research questions and friction points this paper is trying to address.
quantum local recovery
impure codes
pure bounds
CSS codes
stabilizer codes
Impure codes exceeding the pure bounds for quantum local recovery
🤖 AI Summary
This work addresses a critical gap in the theoretical understanding of quantum locally recoverable codes by focusing on non-pure codes, whose performance limits remain poorly characterized compared to pure codes. We construct a new family of non-pure CSS quantum locally recoverable codes based on J-affine variety codes and demonstrate, for the first time, that non-pure codes can surpass the known bounds established for pure codes. By integrating tools from algebraic geometry with quantum error correction theory, we rigorously analyze the local recoverability and minimum distance of the proposed codes and uncover their intrinsic connection to the weight-restricted stabilizer code bound. The constructed non-pure codes exhibit significant improvements over existing pure-code bounds across key parameters, including the number of logical qubits, code length, distance, and locality.
📝 Abstract
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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
impure quantum codes
local recovery
J-affine variety codes
CSS codes
quantum code bounds
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