arXiv subjects

Alina Dubrovska Vasilieva

Publications and source records attributed to Alina Dubrovska Vasilieva.

3 recordsLinked to original sources

arXiv2006

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

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.

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arXiv2006

Properties and Application of Nondeterministic Quantum Query Algorithms

Many quantum algorithms can be analyzed in a query model to compute Boolean functions where input is given by a black box. As in the classical version of decision trees, different kinds of quantum query algorithms are possible: exact, zero-error, bounded-error and even nondeterministic. In this paper, we study the latter class of algorithms. We introduce a fresh notion in addition to already studied nondeterministic algorithms and introduce dual nondeterministic quantum query algorithms. We examine properties of such algorithms and prove relations with exact and nondeterministic quantum query algorithm complexity. As a result and as an example of the application of discovered properties, we demonstrate a gap of n vs. 2 between classical deterministic and dual nondeterministic quantum query complexity for a specific Boolean function.

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arXiv2006

Computing Boolean Functions: Exact Quantum Query Algorithms and Low Degree Polynomials

In this paper we study the complexity of quantum query algorithms computing the value of Boolean function and its relation to the degree of algebraic polynomial representing this function. We pay special attention to Boolean functions with quantum query algorithm complexity lower than the deterministic one. Relation between the degree of representing polynomial and potentially possible quantum algorithm complexity has been already described; unfortunately, there are few examples of quantum algorithms to illustrate theoretical evaluation of the complexity. Work in this direction was aimed (1) to construct effective quantum query algorithms for computing Boolean functions, (2) to design methods for Boolean function construction with a large gap between deterministic complexity and degree of representing polynomial. In this paper we present our results in both directions.

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