Properties and Application of Nondeterministic Quantum Query Algorithms

Many quantum algorithms can be analyzed in a query model to compute Boolean functions where input is given by a black box. As in the classical version of decision trees, different kinds of quantum query algorithms are possible: exact, zero-error, bounded-error and even nondeterministic. In this paper, we study the latter class of algorithms. We introduce a fresh notion in addition to already studied nondeterministic algorithms and introduce dual nondeterministic quantum query algorithms. We examine properties of such algorithms and prove relations with exact and nondeterministic quantum query algorithm complexity. As a result and as an example of the application of discovered properties, we demonstrate a gap of n vs. 2 between classical deterministic and dual nondeterministic quantum query complexity for a specific Boolean function.Comment: 12 pages, 9 figure

Quantum Query Algorithms

Elektroniskā versija nesatur pielikumusLELDE LĀCE KVANTU VAICĀJOŠIE ALGORITMI ANOTĀCIJA Kvantu skaitļošana ir datorzinātņu apakšnozare, kurā tiek izmantotas kvantu mehānikas īpatnības, lai efektīvāk risinātu skaitļošanas uzdevumus. Šajā darbā tiek aplūkoti kvantu vaicājošie algoritmi Bula funkciju rēķināšanai. Darba sākumā tiek pierādīti kvantu algoritmu apakšējie novērtējumi dažādām funkcijām, kas apraksta grafu problēmas. Promocijas darba galvenais uzdevums ir izveidot efektīvus kvantu vaicājošos algoritmus. Ir nodefinēts kā veidot precīzus kvantu vaicājošos algoritmus ar sarežģītību n-1, 2n/3 un n/2. Darba turpinājumā tiek analizēti nedeterminētie kvantu algoritmi ar vienu jautājumu, to veidošanas iespējas un īpašības. Promocijas darbā tiek definēts jauns kvantu vaicājošo algoritmu veids - kvantu vaicājošie algoritmi ar pēcatlasi un tiek pierādīta šo algoritmu saistība ar nedeterminētajiem kvantu vaicājošajiem algoritmiem.LELDE LĀCE QUANTUM QUERY ALGORITHMS ANNOTATION Quantum computing is the subfield of computer science that aims to employ effects of quantum mechanics to efficiently perform computational tasks. The main research object of this work is quantum query model to compute Boolean functions. At first we prove higher lower bounds of quantum query algorithms for some of graph problems. Main purpose of the research is to find quantum query algorithms with complexity lower than deterministic one. The work presents a set of new exact quantum algorithms with quantum query complexity n-1, 2n/3 and n/2. We construct some nondeterministic quantum query algorithms with complexity 1 for Boolean functions with 2, 4 and 2n variables and study some properties of these functions. We propose definition of postselection quantum query algorithm and we propose one method how to make postselection quantum query algorithms