Ohzeki Masayuki
Graduate School of Information Science, Tohoku University, Sendai, Japan.
Institute of Innovative Research, Tokyo Institute of Technology, Kanagawa, Japan.
Sci Rep. 2020 Feb 20;10(1):3126. doi: 10.1038/s41598-020-60022-5.
Quantum annealing is a generic solver for optimization problems that uses fictitious quantum fluctuation. The most groundbreaking progress in the research field of quantum annealing is its hardware implementation, i.e., the so-called quantum annealer, using artificial spins. However, the connectivity between the artificial spins is sparse and limited on a special network known as the chimera graph. Several embedding techniques have been proposed, but the number of logical spins, which represents the optimization problems to be solved, is drastically reduced. In particular, an optimization problem including fully or even partly connected spins suffers from low embeddable size on the chimera graph. In the present study, we propose an alternative approach to solve a large-scale optimization problem on the chimera graph via a well-known method in statistical mechanics called the Hubbard-Stratonovich transformation or its variants. The proposed method can be used to deal with a fully connected Ising model without embedding on the chimera graph and leads to nontrivial results of the optimization problem. We tested the proposed method with a number of partition problems involving solving linear equations and the traffic flow optimization problem in Sendai and Kyoto cities in Japan.
量子退火是一种利用虚拟量子涨落来解决优化问题的通用求解器。量子退火研究领域最具开创性的进展是其硬件实现，即所谓的量子退火器，它使用人工自旋。然而，人工自旋之间的连接在一种称为嵌合体图的特殊网络上是稀疏且有限的。已经提出了几种嵌入技术，但代表要解决的优化问题的逻辑自旋数量大幅减少。特别是，一个包含完全或甚至部分连接自旋的优化问题在嵌合体图上的可嵌入规模较低。在本研究中，我们提出了一种替代方法，通过统计力学中一种著名的方法——哈伯德 - 斯特拉托诺维奇变换或其变体，来解决嵌合体图上的大规模优化问题。所提出的方法可用于处理完全连接的伊辛模型，而无需在嵌合体图上进行嵌入，并能得出优化问题的重要结果。我们用一些涉及求解线性方程的划分问题以及日本仙台和京都城市的交通流优化问题对所提出的方法进行了测试。
