Quantum Algorithms Related to HN-Transforms of Boolean Functions
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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 2ᶯ possible HN-spectra of a Boolean function in n variables, each containing 2 ᶯn elements (i.e., in total 2²ᶯ values in transformed domain) can be computed in O(2²ᶯ) time (more specific with little less than 2²ᶯ+1 arithmetic 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.
The article of record as published may be found at http://link.springer.com/content/pdf/10.1007/978-3-319-55589-8.pdf#page=325
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