Mr. Raghavendra Yelisetty
Quantum Computing Enhances the Performance of Algorithms for Optimal Path Discovery
Graph theory is a core discipline within mathematics and computer science that examines the interconnections between vertices (or points) through edges (or connections). It is widely applied to model various real-world scenarios such as network communication, social interactions, and transport infrastructures. Graphs can either be directed (where edges have a defined direction) or undirected (where edges have no direction), and they can also be weighted, which means edges are assigned values representing factors such as costs, distances, or other parameters. A common challenge in graph theory is determining the shortest route between two vertices in a graph. This concept is applicable in numerous practical fields, such as GPS navigation, computer networks, and optimization tasks. The shortest path is the one that minimizes the cumulative weight of the edges between the two vertices. One popular method for solving this problem is an algorithm that calculates the shortest path between vertices. The process involves assigning an initial distance value to each vertex, setting the start vertex’s value to zero and the rest to infinity. The start vertex is then marked as the current one. For each neighboring vertex, a tentative distance is computed, and if this is smaller than the previously known distance, the new shorter distance is recorded. Once all neighboring vertices are examined, the current vertex is marked as "visited" and the algorithm proceeds to the next unvisited vertex with the smallest tentative distance. This process repeats until the destination vertex is reached, or all vertices are visited. The algorithm for this problem provides an efficient approach for graphs with positive edge weights, with a time complexity of O(V^2) for a simple approach and O(E + V log V) when using a priority queue. This method is essential for optimizing data flow in distributed systems, ensuring effective management and consistency across multiple nodes. This study explores the use of quantum computing to implement the shortest path problem, offering a reduction in time complexity for faster results.