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

A Practical and Scalable Decoder for Topological Quantum Error Correction with Digital Annealer