Nithin Raveendran
Ankur Raina
Narayanan Rengaswamy
Bane Vasic
Francisco Garcia Herrero

Quantum low-density parity check (QLDPC) codes are the only known class of quantum codes in the stabilizer family that have asymptotically nonzero rates and are an important cog in realizing scalable, fault tolerant quantum computation. However, traditional belief propagation (BP) decoding algorithms perform poorly with loopy Tanner graphs and symmetric degenerate errors, which is a big hindrance in achieving high performance in quantum computing and communications. Furthermore, most existing work on decoding QLDPC codes rely on classical BP decoding where one computes marginals of the noisy code word state on the “factor-graph” defined by stabilizer generators. The goal of the proposed research is to develop efficient and fault-tolerant decoders for finite-length QLDPC codes leveraging on our prior work on harmful configurations in factor-graph called trapping sets, identifying quantum equivalent of trapping sets, and utilizing them to improve fault-tolerant thresholds, and ultimately developing BP and more advanced decoding algorithms that employ classical-quantum messages, to harness the full potential of QLDPC codes.

• BibTeX B. Vasić, X. Xiao, and S. Lin, "Learning to Decode LDPC Codes with Finite-Alphabet Message Passing," Information Theory and Applications Workshop (ITA 2018), Feb. 11-16 2018, pp. 1-10.