Evaluation on Quantum Computation and Classic Parallel Approaches for Finding Estimation of the Length of Shortest Path in a Weighted Graph

In this paper we evaluate our presented Quantum Approach for finding the Estimation of the Length of the Shortest Path in a Connected Weighted Graph which is achieved with a polynomial time complexity about O(n) and as a result of evaluation we show that the Probability of Success of our presented Quantum Approach is increased if the Standard Deviation of the Length of all possible paths between Source and Target vertices is increased also we show that if the Standard Deviation is low nevertheless our Quantum Computation Approach is satisfactory and even the standard deviation is exactly zero the probability of Success of our Quantum Approach is not only zero but also is %100. Also we present a Classic Parallel Approach for finding the Estimation of the Length of the shortest path and then as a comparison between our Quantum Computation and Classic Parallel Approaches we show that even by applying the Classic Parallel Approach the problem can be solved with time complexity about O(log(2n -1)).