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 sarežitiba Abstract
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