Solving the General Planar Graph Coloring Problem Using Grover's Algorithm

Abstract

In this paper, we discuss the structure and implementations of the planar graph-coloring problem (PGCP). We briefly look at well-known classical algorithms used to solve the PGCP but primarily focus on the quantum computational angle. Grover’s search is a well-known quantum algorithm that offers a quadratic advantage relative to its classical counterparts. We inspect its application to the PGCP and build a corresponding quantum circuit. We take a specific case of specialists in Nepalese hospitals and optimize their placements.