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Breaking limitation of quantum annealer in solving optimization problems under constraints
arXiv - CS - Discrete Mathematics Pub Date : 2020-02-13 , DOI: arxiv-2002.05298
Masayuki Ohzeki

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.

中文翻译:

突破量子退火器在约束条件下求解优化问题的局限性

量子退火是使用虚拟量子涨落的优化问题的通用求解器。量子退火研究领域最具突破性的进展是其硬件实现,即所谓的量子退火器,使用人工自旋。然而,人工自旋之间的连接是稀疏的,并且受限于一个称为嵌合图的特殊网络。已经提出了几种嵌入技术,但是代表要解决的优化问题的逻辑自旋的数量急剧减少。特别是,包括完全或什至部分连接的自旋的优化问题在嵌合图上的可嵌入大小较低。在目前的研究中,我们提出了一种替代方法,通过称为 Hubbard-Stratonovich 变换或其变体的统计力学中众所周知的方法来解决嵌合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 Ising 模型,无需嵌入嵌合图,并导致优化问题的非平凡结果。我们在日本仙台和京都城市用许多涉及求解线性方程和交通流优化问题的分区问题测试了所提出的方法。
更新日期:2020-02-14
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