Quantum Query Algorithms for Certain Problems and Generalization of Algorithm Designing Techniques

Abstract

Quantum algorithms can be analyzed in a query model to compute Boolean functions where input is given in a black box, but the aim is to compute function value for arbitrary input using as few queries as possible. In this paper we concentrate on quantum query algorithm designing tasks. The main aim of research was to find new efficient algorithms and develop general algorithm designing techniques. We present several exact quantum query algorithms for certain problems that are better than classical counterparts. Next we introduce algorithm transformation methods that allow significant enlarging of sets of exactly computable functions. Finally, we propose algorithm constructing methods applicable for algorithms with specific properties that allow constructing algorithms for more complex functions preserving acceptable error probability and number of queries.