Dynamic Grover Search: Applications in Recommendation systems and Optimization problems

In the recent years we have seen that Grover search algorithm [1] by using quantum parallelism has revolutionized the field of solving huge class of NP problems in comparison to classical systems. In this work we explore the idea of extending the Grover search algorithm to approximate algorithms. Here we try to analyze the applicability of Grover search to process an unstructured database with dynamic selection function as compared to the static selection function in the original work[1]. This allows us to extend the application of Grover search to the field of randomized search algorithms. We further use the Dynamic Grover search algorithm to define the goals for a recommendation system, and define the algorithm for recommendation system for binomial similarity distribution space giving us a quadratic speedup over traditional unstructured recommendation systems. Finally we see how the Dynamic Grover Search can be used to attack a wide range of optimization problems where we improve complexity over existing optimization algorithms.