论文标题
使用数字退火器校正拓扑量子误差的实用且可扩展的解码器
A Practical and Scalable Decoder for Topological Quantum Error Correction with Digital Annealer
论文作者
论文摘要
量子误差校正是实现大规模量子计算的最重要里程碑之一。为了实现这一目标,不仅要整合大量具有高保真度的量子位,而且要构建可以执行误差校正的可扩展经典系统。在这里,我们提出了一个有效且可扩展的解码器,用于使用Fujitsu Digital Exealer(DA)进行量子误差校正。具体而言,稳定器代码的误差校正问题被映射到ISING型优化问题,所谓的二次不受约束的二进制优化(QUBO)问题,该问题由DA解决。特别是,我们为表面代码实施了建议的DA解码器,并对各种代码距离执行详细的数值实验,以查看其性能和可扩展性。我们观察到,在所有测试条件下,使用模拟退火(SA)和最小重量匹配(MWPM)算法的解码方法比解码方法的计算缩放量比解码方法具有较低的多项式。还表明,DA解码器从包括硬件实现在内的各个角度来看,与联合信息(UF)解码器具有优势。此外,分析了DA解码器的逻辑误差概率的阈值行为,并且所得阈值在9.4%和9.8%之间,这非常接近MWPM解码器获得的阈值。该结果清楚地表明了DA解码器对量子误差校正的高潜力。
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.