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A Brief Study on Quantum Walks and Quantum Mechanics
Published in Thiruselvan Subramanian, Archana Dhyani, Adarsh Kumar, Sukhpal Singh Gill, Artificial Intelligence, Machine Learning and Blockchain in Quantum Satellite, Drone and Network, 2023
Sapna Renukaradhya, Preethi, Rupam Bhagawati, Thiruselvan Subramanian
The quantum walk is a quantum counterpart of the conventional random walk that is used in quantum computing (also known as quantum walk). In comparison to regular computers, quantum walk, which takes advantage of the phenomenon of quantum superposition [9], provides an exponential algorithmic speedup. Despite the fact that many years have passed and various improvements have been made, and some of the unresolved problems have been thoroughly explored and answered [10,11], further study is still required for proper examination of the quantum walk phenomenon. Search results for Google’s search engine may be found by using the PageRank algorithm [12], which performs a random walk through a network with vertices representing different websites to identify relevant results. Rather than just exploring the internet at random, it uses this method to evaluate the relevance of every given piece of information. According to research, the PageRank algorithm has been customised in a number of ways, including the use of personalised PageRank [13,14]. Other novel algorithms, such as Random Walk with Restart (RWR) [15] and Lazy Random Walk (LRW) [16], are proposed in addition to walk rules.
Future Semiconductor Devices
Published in Lambrechts Wynand, Sinha Saurabh, Abdallah Jassem, Prinsloo Jaco, Extending Moore’s Law through Advanced Semiconductor Design and Processing Techniques, 2018
Wyn Lambrechts, Saurabh Sinha, Jassem Abdallah, Jaco Prinsloo
A quantum walk is the quantum version of the random walk computed with classical algorithms. A random walk is typically applied in the context of simulation, e.g. where successive movements based on given movements are determined probabilistically. A typical example of such a probabilistic movement model is the random motion of particles resulting from collision with other particles, a phenomenon called Brownian motion. Random walks can be either discreet or continuous, depending on the structure of time in which the movement is considered. While classical random walks describe particle position as definitive and certain, quantum walks describe particle position as a superposition. Quantum walks can have many advanced applications in solving computational problems in the fields of mathematics, quantum physics and computer sciences (Akama 2015).
Optimal sensor spacing in IoT network based on quantum computing technology
Published in International Journal of Parallel, Emergent and Distributed Systems, 2023
Gopal Krishna, Anish Kumar Saha
The GT is a tree structure obtained by combining two trees by connecting the nodes of one tree to exactly two nodes of the other tree. Introducing quantum walk into the GT graphs improves the traversal speed by accurately determining the right path that offers minimised error rates. The traversal begins on the left and ends on the right side of the graph. The probability of reaching the destination is higher than the classical random walks. Thus, the quantum walk can be introduced into the GT to reduce the error rates and improve the data accuracy rates. To enumerate it, the graphs are considered columns, with all nodes maintaining an equal distance between the entrance and exit nodes. The columns present in the graphs consist of the sensor nodes, and the columns can be labelled as where indicates the tree’s height. For instance, the column consists of the nodes with the shortest path or the optimal path from the root node to the destination, then the state of the column is represented as follows: Where, indicates a column with nodes , and the factor is responsible for ensuring that the state is normalised. Through the application of the adjacency matrix in the above formulation, the state can be represented as follows: Where, indicates the weight value added to edges other than the columns . For the columns , the weight value is 2. For infinite lines, the probability will be computed for the zigzag movement at a distance with a state .