  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.
