Suksmono Andriyan Bayu
Telecommunication Engineering Scientific and Research Group (TESRG), School of Electrical Engineering and Informatics and The Research Center on Information and Communication Technology (PPTIK-ITB), Institut Teknologi Bandung, Jl. Ganesha No.10, Bandung 40132, Indonesia.
Entropy (Basel). 2018 Feb 22;20(2):141. doi: 10.3390/e20020141.
Hard problems have recently become an important issue in computing. Various methods, including a heuristic approach that is inspired by physical phenomena, are being explored. In this paper, we propose the use of simulated quantum annealing (SQA) to find a Hadamard matrix, which is itself a hard problem. We reformulate the problem as an energy minimization of spin vectors connected by a complete graph. The computation is conducted based on a path-integral Monte-Carlo (PIMC) SQA of the spin vector system, with an applied transverse magnetic field whose strength is decreased over time. In the numerical experiments, the proposed method is employed to find low-order Hadamard matrices, including the ones that cannot be constructed trivially by the Sylvester method. The scaling property of the method and the measurement of residual energy after a sufficiently large number of iterations show that SQA outperforms simulated annealing (SA) in solving this hard problem.
近年来，难题已成为计算领域的一个重要问题。人们正在探索各种方法，包括一种受物理现象启发的启发式方法。在本文中，我们提出使用模拟量子退火（SQA）来寻找哈达玛矩阵，这本身就是一个难题。我们将该问题重新表述为通过完全图连接的自旋向量的能量最小化问题。计算基于自旋向量系统的路径积分蒙特卡罗（PIMC）SQA进行，施加一个随时间强度降低的横向磁场。在数值实验中，所提出的方法被用于寻找低阶哈达玛矩阵，包括那些不能通过西尔维斯特方法平凡构造的矩阵。该方法的缩放性质以及在足够多次迭代后的残余能量测量表明，在解决这个难题方面，SQA优于模拟退火（SA）。
