Finding Hadamard Matrices by a Quantum Annealing Machine

Finding a Hadamard matrix (H-matrix) among the set of all binary matrices of corresponding order is a hard problem, which potentially can be solved by quantum computing. We propose a method to formulate the Hamiltonian of finding H-matrix problem and address its implementation limitation on existing...

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Bibliographic Details
Published in:Scientific reports 2019-10, Vol.9 (1), p.14380-12, Article 14380
Main Authors: Suksmono, Andriyan Bayu, Minato, Yuichiro
Format: Article
Language:English
Subjects:
639/766/259
639/766/483/481
Humanities and Social Sciences
multidisciplinary
Science
Science (multidisciplinary)
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Summary:Finding a Hadamard matrix (H-matrix) among the set of all binary matrices of corresponding order is a hard problem, which potentially can be solved by quantum computing. We propose a method to formulate the Hamiltonian of finding H-matrix problem and address its implementation limitation on existing quantum annealing machine (QAM) that allows up to quadratic terms, whereas the problem naturally introduces higher order ones. For an M -order H-matrix, such a limitation increases the number of variables from M 2 to ( M 3  +  M 2  −  M )/2, which makes the formulation of the Hamiltonian too exhaustive to do by hand. We use symbolic computing techniques to manage this problem. Three related cases are discussed: (1) finding N  
ISSN:2045-2322
2045-2322
DOI:10.1038/s41598-019-50473-w