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Quantum search algorithm
Mejdrech, Lukáš ; Barto, Libor (advisor) ; Holub, Štěpán (referee)
In this work we study Grover's algorithm for quantum computers. This algorithm promises to search in an unstructured database in time comparable with a square root of the number of objects. A description of basic quantum computer principles is followed by the original Grover's formulation and a proof of the algorithm, as well as a later geometrical description of the algorithm. We also mention their suitability for educational purposes. We also include a description of the Grover's algorithm in a programming language, which makes it possible to simulate a quantum computing on classical computers.
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Varieties of superalgebras
Lišková, Adéla ; Žemlička, Jan (advisor) ; Barto, Libor (referee)
The goal of the thesis is to introduce the basics of the theory of superalgebras, that is Z2-graded algebras over a field of characteristic different from two, as well as to present necessary basics of universal and multilinear algebra, especially the tensor product and the terms variety of algebra and ideal of identities. We present the definitions of algebra and superalgebra including examples, we then look into the tensor product of superalgebras and its properties, Clifford and Grassmann superalgebras. A part of the thesis is dedicated to the construction of the free nonassociative algebra and the clarification of the relationship between varieties of algebras and ideals of identities including the specification of said relationship for superalgebras. The thesis also deals with varieties of superalgebras. 1
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