Abstract
In this study, a new methodology based on the Hadamard matrix is proposed to construct quantum Boolean functions f such that \(f = {I_{{2^n}}} - 2{P_{{2^n}}}\), where \({I_{{2^n}}}\) is an identity matrix of order 2n and \({P_{{2^n}}}\) is a projective matrix with the same order as \({I_{{2^n}}}\). The enumeration of this class of quantum Boolean functions is also presented.
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Supported by the National Natural Science Foundation of China (Nos. 11171093, U1404601, 11471104, 61402154, 61170270, 11501181, 11571094, 61572081); Program for Innovative Research Team (in Science and Technology) in University of Henan Province (No.14IRTSTHN023), Ph.D research startup foundation of Henan Normal University (Grant No. 5101019170133). The basic and Cutting-edge Technology Research projects of Science and Technology Department of Henan Province(No.132300410430).
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Du, J., Pang, Sq., Wen, Qy. et al. Construction of a class of quantum Boolean functions based on the Hadamard matrix. Acta Math. Appl. Sin. Engl. Ser. 31, 1013–1020 (2015). https://doi.org/10.1007/s10255-015-0523-z
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DOI: https://doi.org/10.1007/s10255-015-0523-z