A hierarchical sorting oracle

Abstract

Classical tree search algorithms mimic the problem solving capabilities traditionally performed by humans. In this work we propose a unitary operator, based on the principles of reversible computation, focusing on hierarchical tree search concepts for sorting purposes. These concepts are then extended in order to build a quantum oracle which, combined with Grover's quantum algorithm, can be employed as a quantum hierarchical search mechanism whilst taking advantage of a quadratic speedup. Finally, we show how the developed model can be extended in order to perform a N-level depth-limited search. © 2011 Springer-Verlag.