Quantum computing and Grover\u27s algorithm

Magistrsko delo obravnava teoretičen pristop k razumevanju kvantnega računalništva in opisuje kvantni algoritem kot primer uporabnosti hitro se razvijajočega področja. Delo je razdeljeno na štiri dele. V prvem delu je podrobneje opisana matematična podlaga, potrebna za razumevanje kvantnega računanja, ki obsega kompleksna števila, vektorske prostore in razširitve ter linearne transformacije. Drugi del opisuje fizikalne osnove in temeljne definicije ter razlage kvantne mehanike, iz katere se razvija področje kvantnega računalništva. Kvantni mehaniki sledi poglavje kvantnega računalništva, v katerem so predstavljeni osnovni koncepti in elementi, s katerimi je možno graditi kvantne algoritme. Predstavljen je tudi model kvantnega računanja, katerega se poslužujejo raziskovalci in razvijalci na področju odkrivanja novih kvantnih algoritmov. V zadnjem delu magistrske naloge je opisan Groverjev algoritem, eden izmed prvih kvantnih algoritmov, ki prikazuje uporabnost kvantnega računalništva v prihodnosti.The master thesis investigates a theoretical approach to the understanding of quantum computing and describes quantum algorithm as an example of usability in a rapidly evolving field. The thesis is divided into four parts. In the first part, the mathematical basis needed to understand quantum computation, comprising complex numbers, vector spaces and extensions, along with linear transformations, is described in more detail. The second part describes the physical basics and basic definitions and explanations of quantum mechanics, from which the field of quantum computing develops. Then follows the chapter of quantum computing, in which the basic concepts and elements for constructing quantum algorithms are presented. In this chapter quantum computing model is described. It is used by researchers and developers in the field of discovering new quantum algorithms. In the last part of the master\u27s thesis, one of the first quantum algorithms, Grover\u27s algorithm, is described, which presents the usability of quantum computing in the future