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Recent developments have shown the existence of quantum low-density paritycheck (qLDPC) codes with constant rate and linear distance. A natural questionconcerns the efficient decodability of these codes. In this paper, we present alinear time decoder for the recent quantum Tanner codes construction ofasymptotically good qLDPC codes, which can correct all errors of weight up to aconstant fraction of the blocklength. Our decoder is an iterative algorithmwhich searches for corrections within constant-sized regions. At each step, thecorrections are found by reducing a locally defined and efficiently computablecost function which serves as a proxy for the weight of the remaining error.

An efficient decoder for a linear distance quantum LDPC code