  Quantum low-density parity-check (LDPC) codes, a class of quantum error
correcting codes, are considered a blueprint for scalable quantum circuits. To
use these codes, one needs efficient decoding algorithms. In the classical
setting, there are multiple efficient decoding algorithms available, including
Viderman's algorithm (Viderman, TOCT 2013). Viderman's algorithm for classical
LDPC codes essentially reduces the error-correction problem to that of
erasure-correction, by identifying a small envelope $L$ that is guaranteed to
contain the error set.
  Our main result is a generalization of Viderman's algorithm to quantum LDPC
codes, namely hypergraph product codes (Tillich, Z\'emor, IEEE T-IT, 2013).
This is the first erasure-conversion algorithm that can correct up to
$\Omega(D)$ errors for constant-rate quantum LDPC codes, where $D$ is the
distance of the code. In that sense, it is also fundamentally different from
existing decoding algorithms, in particular from the small-set-flip algorithm
(Leverrier, Tillich, Z\'emor, FOCS, 2015). Moreover, in some parameter regimes,
our decoding algorithm improves on the decoding radius of existing algorithms.
We note that we do not yet have linear-time erasure-decoding algorithms for
quantum LDPC codes, and thus the final running time of the whole decoding
algorithm is not linear; however, we view our linear-time envelope-finding
algorithm as an important first step.
