  Quantum LDPC codes are a promising direction for low overhead quantum
computing. In this paper, we propose a generalization of the Union-Find decoder
as adecoder for quantum LDPC codes. We prove that this decoder corrects all
errors with weight up to An^{\alpha} for some A, {\alpha} > 0 for different
classes of quantum LDPC codes such as toric codes and hyperbolic codes in any
dimension D \geq 3 and quantum expander codes. To prove this result, we
introduce a notion of covering radius which measures the spread of an error
from its syndrome. We believe this notion could find application beyond the
decoding problem. We also perform numerical simulations, which show that our
Union-Find decoder outperforms the belief propagation decoder in the low error
rate regime in the case of a quantum LDPC code with length 3600.
