Quantum Query Algorithm Constructions for Computing AND, OR and MAJORITY Boolean Functions

TL;DR

This paper develops new quantum query algorithms and techniques for efficiently computing Boolean functions like AND, OR, and MAJORITY, advancing quantum algorithm design methods.

Contribution

It introduces exact quantum algorithms surpassing classical ones and presents transformation methods to expand computable function sets and design complex algorithms.

Findings

Quantum algorithms outperform classical counterparts for certain Boolean functions.

Transformation methods significantly enlarge the set of exactly computable functions.

Proposed design methods enable constructing complex algorithms from simpler sub-functions.

Abstract

Quantum algorithms can be analyzed in a query model to compute Boolean functions where input is given in a black box and the aim is to compute function value for arbitrary input using as few queries as possible. We concentrate on quantum query algorithm designing tasks in this paper. The main aim of the research was to find new efficient algorithms and develop general algorithm designing techniques. First, 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 exactly computable functions sets. Finally, we propose quantum algorithm designing methods. Given algorithms for the set of sub-functions, our methods use them to design a more complex one, based on algorithms described before. Methods are applicable for input algorithms with specific properties and preserve acceptable error probability and number of queries. Methods offer constructions for computing AND, OR and MAJORITY kinds of Boolean functions.