基于量子退火的稀疏矩阵排序方法及其参数整定

Tomoko Komiyama, Tomohiro Suzuki
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引用次数: 2

摘要

量子退火实现了专门用于组合优化问题(COPs)的量子计算机。将COP表示为哈密顿量,量子退火通过寻找哈密顿量的基态得到解。找到解决方案的难易程度取决于在制定问题时分配给成本函数和约束函数的权重。换句话说,参数调整在解决量子退火问题中是必不可少的。本文将稀疏直接求解器中寻找减少填充的排序问题表述为哈密顿量,并利用量子退火方法求解该问题。讨论了参数整定在量子退火求解cop问题中的必要性和有效性。经过权值调优后的结果表明,对于${5\,\times \,5}$矩阵,我们可以将获得最优解的率提高94%,对于${6\,\times \,6}$矩阵,我们可以提高68%,对于${7\,\times \,7}$矩阵,我们可以提高27%。此外,研究表明,给我们想要满足的约束赋予较高的权重并不会提供最优解。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Sparse Matrix Ordering Method with a Quantum Annealing Approach and its Parameter Tuning
Quantum annealing realizes quantum computers specialized for combinatorial optimization problems (COPs). A COP is formulated as a Hamiltonian, and quantum annealing obtains a solution by finding the ground state of the Hamiltonian. The ease of finding a solution depends on the weights assigned to the cost and constraint functions when formulating the problem. In other words, parameter tuning is essential in solving problems with quantum annealing. In the present paper, the problem of searching an ordering that reduces the fill-in for a sparse direct solver is formulated as a Hamiltonian, and quantum annealing finds the solution to this problem. We discuss the necessity and effectiveness of parameter tuning for solving COPs with quantum annealing. The results after weight tuning show that we can improve the rate of an optimal solution obtained by a maximum of 94% for ${5\,\times \,5}$ matrices, 68% for ${6\,\times \,6}$ matrices, and 27% for ${7\,\times \,7}$ matrices. Moreover, it is shown that giving high weights to the constraints we want to satisfy will not provide an optimal solution.
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