  Quantum error correction is one of the most important milestones for
realization of large-scale quantum computation. To achieve this, it is
essential not only to integrate a large number of qubits with high fidelity,
but also to build a scalable classical system that can perform error
correction. Here, we propose an efficient and scalable decoder for quantum
error correction using Fujitsu Digital Annealer (DA). Specifically, the error
correction problem of stabilizer codes is mapped into an Ising-type
optimization problem, so-called quadratic unconstrained binary optimization
(QUBO) problem, which is solved by DA. In particular, we implement the proposed
DA decoder for the surface code and perform detailed numerical experiments for
various code distances to see its performance and scalability. We observe that
computational scaling for the DA decoder has a lower order of polynomial than
the decoding methods using simulated annealing (SA) and minimum-weight perfect
matching (MWPM) algorithm under all tested conditions. It is also shown that
the DA decoder has advantages over the Union-Find (UF) decoder from a variety
of perspectives including hardware implementation. Furthermore, the threshold
behavior of the logical error probability for the DA decoder is analyzed and
the resultant threshold lies between 9.4% and 9.8%, which is very close to that
obtained by the MWPM decoder. This result clearly shows the high potential of
the DA decoder for quantum error correction.
