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Quantum version of self-balanced binary search tree with strings as keys and applications

In this paper, we present the data structure that implements the Self-Balanced Binary Search Tree with strings as keys and quantum comparing procedure. We cannot use the standard Self-Balanced Binary Search because of an error probability for the quantum comparing procedure. We can solve the issue using the standard success probability boosting technique. The presented data structure is more effective (in terms of running time) than using boosting technique. We apply the data structure for the Most Frequently String problem. So, we obtain a quantum algorithm for the problem that is faster than the existing quantum algorithm, and the best classical algorithm in the case of a significant part of the input strings (we mean O(n)) has a length that is at least ω((log n)2). Here n means the number of strings in a collection.