Quantum Existence Testing and Its Application for Finding Extreme Values in Unsorted Databases

Many information processing and computing problems can be traced back to find the extreme value of a database or a function. Unfortunately, classical solutions suffer from high computational complexity if the database is unsorted or, equivalently, the function has many local minimum/maximum points. Proposed quantum computing-based solutions involve the repeated application of Grower´s searching algorithm. In this paper, we introduce a new technique exploiting the parallel processing capabilities of quantum computing in a different way. We derive a special case of quantum counting - we call it quantum existence testing - which allows adapting the classical logarithmic search algorithm so that it is suitable for structured databases to unstructured ones. The paper analyzes the required number of database queries, the corresponding computational complexity, and the probability of error and their relationship