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Finding a Hadamard Matrix by Simulated Quantum Annealing

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 2018, 20(2), 141; https://doi.org/10.3390/e20020141
Received: 2 January 2018 / Revised: 6 February 2018 / Accepted: 16 February 2018 / Published: 22 February 2018
(This article belongs to the Special Issue Quantum Information and Foundations)
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. View Full-Text
Keywords: quantum annealing; adiabatic quantum computing; hard problems; Hadamard matrix; binary optimization quantum annealing; adiabatic quantum computing; hard problems; Hadamard matrix; binary optimization
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Suksmono, A.B. Finding a Hadamard Matrix by Simulated Quantum Annealing. Entropy 2018, 20, 141.

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