Dynamic Grover Search: Applications in Recommendation systems and Optimization problems

TL;DR

This paper extends Grover's quantum search algorithm to dynamic and approximate scenarios, applying it to recommendation systems and optimization problems, achieving quadratic speedups over classical methods.

Contribution

It introduces a dynamic version of Grover's search algorithm for unstructured data and demonstrates its application in recommendation systems and optimization tasks.

Findings

Quadratic speedup in recommendation algorithms.

Effective application of dynamic Grover search to optimization problems.

Extension of Grover's algorithm to approximate and dynamic contexts.

Abstract

In the recent years, we have seen that Grover search algorithm (Proceedings, 28th annual ACM symposium on the theory of computing, pp. 212-219, 1996) by using quantum parallelism has revolutionized the field of solving huge class of NP problems in comparisons to classical systems. In this work, we explore the idea of extending Grover search algorithm to approximate algorithms. Here we try to analyze the applicability of Grover search to process an unstructured database with a dynamic selection function in contrast to the static selection function used in the original work (Grover in Proceedings, 28th annual ACM symposium on the theory of computing, pp. 212-219, 1996). We show that this alteration facilitates us to extend the application of Grover search to the field of randomized search algorithms. Further, we use the dynamic Grover search algorithm to define the goals for a recommendation system based on which we propose a recommendation algorithm which uses binomial similarity distribution space giving us a quadratic speedup over traditional classical unstructured recommendation systems. Finally, we see how dynamic Grover search can be used to tackle a wide range of optimization problems where we improve complexity over existing optimization algorithms.