LP Decoding of Quantum Stabilizer Codes

Linear programming (LP) decoding is an approach for decoding classical codes, especially for decoding low-density parity-check codes. In this paper, we initiate the study of LP decoding for stabilizer quantum error-correction codes. In particular, we formulate different polytope relaxations, we introduce pseudoweights to analyze the effect of pseudocodewords, and we give theoretical guarantees of the decoding ability of the LP decoder for the quantum depolarizing channel and for the quantum erasure channel.