Power and Limitations of Linear Programming Decoder for Quantum LDPC Codes

Understand

Decoding quantum error-correcting codes is a key challenge in enabling fault-tolerant quantum computation.

• In the classical setting, linear programming (LP) decoders offer provable performance guarantees and can leverage fast practical optimization algorithms.
• Although LP decoders have been proposed for quantum codes, their performance and limitations remain relatively underexplored.
• In this work, we uncover a key limitation of LP decoding for quantum low-density parity-check (LDPC) codes: certain constant-weight error patterns lead to ambiguous fractional solutions that cannot be resolved through independent rounding.