Quantum algorithms related to HN-transforms of Boolean functions

Document Type

Conference Article

Publication Title

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Abstract

HN-transforms, which have been proposed as generalizations of Hadamard transforms, are constructed by tensoring Hadamard and nega-Hadamard kernels in any order. We show that all the 2npossible HN-spectra of a Boolean function in n variables, each containing 2nelements (i.e., in total 22nvalues in transformed domain) can be computed in O(22n) time (more specific with little less than 22n+1arithmetic operations). We propose a generalization of Deutsch-Jozsa algorithm, by employing HN-transforms, which can be used to distinguish different classes of Boolean functions over and above what is possible by the traditional Deutsch-Jozsa algorithm.

First Page

314

Last Page

327

DOI

10.1007/978-3-319-55589-8_21

Publication Date

1-1-2017

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