Shortest Path through Grovers Algorithm in MATLAB

Nidhi Jain, Dr. Mahesh Porwal

Abstract Classical algorithms have been used to search over some space for finding the shortest paths problem between two points in a network and a minimal weight spanning tree for routing. Any classical algorithm deterministic or probabilistic will clearly used O(N) steps since on the average it will measure a large fraction of N records. Quantum algorithm is the fastest possible algorithm that can do several operations simultaneously due to their wave like properties. This wave gives an O(âˆšN ) steps quantum algorithm for identifying that record, where was used classical Dijkstras algorithm for finding shortest path problem in the graph of network and implement quantum search. Also we proposed the structure for non-classical algorithms and design the various phases of the probabilistic quantum classical algorithm for classical and quantum parts. Finally, we represent the result of implementing and simulating Dijkstras algorithm as the probabilistic quantum-classical algorithm. Keywords: Graph Theory, Algorithm Design, Quantum Algorithm, Network Routing

Title:	Shortest Path through Grovers Algorithm in MATLAB
Author Name:	Nidhi Jain, Dr. Mahesh Porwal
Abstract:	Abstract Classical algorithms have been used to search over some space for finding the shortest paths problem between two points in a network and a minimal weight spanning tree for routing. Any classical algorithm deterministic or probabilistic will clearly used O(N) steps since on the average it will measure a large fraction of N records. Quantum algorithm is the fastest possible algorithm that can do several operations simultaneously due to their wave like properties. This wave gives an O(âˆšN ) steps quantum algorithm for identifying that record, where was used classical Dijkstras algorithm for finding shortest path problem in the graph of network and implement quantum search. Also we proposed the structure for non-classical algorithms and design the various phases of the probabilistic quantum classical algorithm for classical and quantum parts. Finally, we represent the result of implementing and simulating Dijkstras algorithm as the probabilistic quantum-classical algorithm. Keywords: Graph Theory, Algorithm Design, Quantum Algorithm, Network Routing
Cite this article:	Nidhi Jain, Dr. Mahesh Porwal , " Shortest Path through Grovers Algorithm in MATLAB " , International Journal of Emerging Trends & Technology in Computer Science (IJETTCS), Volume 4, Issue 5(2), September - October 2015 , pp. 065-067 , ISSN 2278-6856.
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