Properties and application of nondeterministic quantum query algorithms

Alina Dubrovska

doi:10.1117/12.720641

25 April 2007 Properties and application of nondeterministic quantum query algorithms

Alina Dubrovska

Proceedings Volume 6573, Quantum Information and Computation V; 657310 (2007) https://doi.org/10.1117/12.720641
Event: Defense and Security Symposium, 2007, Orlando, Florida, United States

Abstract

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, with bounded error and even nondeterministic. In this paper, we study the latter class of algorithms. We introduce a new 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. Finally, we show an approach how to construct examples where quantum nondeterministic complexity of an algorithm is O(1), however classical deterministic algorithm for the same function would require O(n) queries.

Citation Download Citation

Alina Dubrovska "Properties and application of nondeterministic quantum query algorithms", Proc. SPIE 6573, Quantum Information and Computation V, 657310 (25 April 2007); https://doi.org/10.1117/12.720641

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