Varbūtisko un kvantu algoritmu sarežģītība
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Latvijas Universitāte
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Abstract
Šajā darbā galvenokārt ir aplūkoti varbūtiskie un kvantu vaicājošie algoritmi Būla funkciju rēķināšanai. Pētījuma mērķis ir atrast efektīvus algoritmus, kā arī salīdzināt dažādus algoritmu modeļus. Ir izpētītas vairākas funkcijas un atrasti efektīvie algoritmi to rēķināšanai. Ir piedāvātas kvantu algoritmu ar ierobežotu kļūdu konstruēšanas metodes, kas balstās uz idejas sadalīt doto problēmu apakš problēmās. Darbā ir izpētīta arī Kušiļeviča funkcija, atrasts kvantu algoritms ar ierobežotu kļūdu tās rēķināšanai.
The problem discussed in this work is related to probabilistic and quantum query algorithms computing Boolean functions. The main aim of the research is to find effective algorithms and compare different models of algorithms. Effective algorithms for several Boolean functions are designed. Methods of constructing bounded-error quantum algorithms are offered. Their main idea is dividing the given problem into subproblems. Kushilevitz’s function is viewed and bounded-error quantum algorithm computing it is found.
The problem discussed in this work is related to probabilistic and quantum query algorithms computing Boolean functions. The main aim of the research is to find effective algorithms and compare different models of algorithms. Effective algorithms for several Boolean functions are designed. Methods of constructing bounded-error quantum algorithms are offered. Their main idea is dividing the given problem into subproblems. Kushilevitz’s function is viewed and bounded-error quantum algorithm computing it is found.