Kvantu vaicājošo algoritmu un komunikāciju protokolu sarežģītība

Abstract

Anotacija Kvantu skaitošana ir datorzinatnes apakšnozare, kas balstas uz kvantu mehanikas likumiem, kuru iespejas un priekšrocibas tiek izmantotas, lai efektivak risinatu skaitošanas uzdevumus. Galvenais darba petamais objekts ir kvantu vaicajošo algoritmu modelis. Petijuma galvenais meris ir efektivo kvantu vaicajošo algoritmu atrašana konkretam problemam, ka ari visparigo algoritmu konstruešanas metožu izstradašana. Ir ieguti rezultati attieciba uz dažadiem kvantu vaicajošo algoritmu tipiem, ka eksaktais algoritms, algoritms ar kudas varbutibu un nedeterminetais algoritms. Promocijas darba pirmaja daa ir apskatiti kvantu eksaktie algoritmi un kvantu algoritmi ar kudas varbutibu Bula funkciju reinašanai. Otraja daa vaicajošo algoritmu modelis ir pielietots daudzvertigu funkciju reinašanai. Treša daa ir veltita nedeterminetiem vaicajošiem algoritmiem. Atslegas vardi: kvantu skaitošana, vaicajošais modelis, algoritmu izstrade, algoritmu sarežitibaAbstract Quantum computing is a method of computation based on the laws of quantum mechanics. This subfield of computer science aims to employ quantum mechanical effects for an efficient performance of computational tasks. The main research object of this effort is the quantum query model. The aim of the present research study is to discover efficient quantum query algorithms for certain problems and develop general techniques for designing algorithms. The study has produced several outcomes regarding different kinds of quantum algorithms: exact, bounded-error, and nondeterministic. In the first part of the thesis, exact and bounded-error quantum query algorithms for computing Boolean functions are presented. In the second part, a query model is applied for computing multivalued functions. The third part is devoted to nondeterministic query algorithms. Keywords: quantum computing, query model, algorithm design, algorithm complexity