Some features of the site may not work correctly. In this article, we give a brief overview of quantum walks, with emphasis on their algorithmic applications. We consider the problem of finding a marked vertex in a graph from an arbitrary starting distribution, using a quantum walk based algorithm. We describe the Grover’s search algorithm and estimate its complexity. However, it is still unclear how to use these novel properties to gain an algorithmic speedup over classical algorithms. When starting…, A Unified Framework of Quantum Walk Search, Quantum Speedup for Graph Sparsification, Cut Approximation and Laplacian Solving, Quadratic speedup for finding marked vertices by quantum walks, Quantum Walks Can Find a Marked Element on Any Graph, Improved quantum backtracking algorithms through effective resistance estimates, Quantum walk speedup of backtracking algorithms, Quantum speed-up of Markov chain based algorithms, Quantum measurements and the Abelian Stabilizer Problem, View 12 excerpts, references methods, results and background, View 4 excerpts, references methods and background, 45th Annual IEEE Symposium on Foundations of Computer Science, By clicking accept or continuing to use the site, you agree to the terms outlined in our. Quantum random walks on graphs have been shown to display many interesting properties, including exponentially fast hitting times when compared with their classical counterparts. You are currently offline. Semantic Scholar is a free, AI-powered research tool for scientific literature, based at the Allen Institute for AI. will be stated as quantum analogues of classical search procedures. Our algorithm outputs a marked vertex in the same runtime up to a logarithmic factor in the number of marked vertices. @article{Piddock2019QuantumWS, title={Quantum walk search algorithms and effective resistance}, author={Stephen Piddock}, journal={arXiv: Quantum Physics}, year={2019} } Stephen Piddock Published 2019 Mathematics, Physics arXiv: Quantum Physics We consider the … The chapter on spatial search algorithms has been rewritten to offer a more comprehensive approach and a new chapter describing the element distinctness algorithm has been added. Quantum walks are quantum counterparts of Markov chains. Quantum walk search algorithms and effective resistance Stephen Piddock December 10, 2019 Abstract We consider the problem of finding a marked vertex in a graph from an arbitrary starting distribution, using a quantum walk based algorithm. Quantum walks, search algorithm and state transfer Author: Stanislav Skoupý Abstract: In this text we focus on the topic of quantum walks and their usage. However, it is still unclear how to use these novel properties to gain an algorithmic speedup over classical algorithms. About this book. It will be shown that this algorithm performs an oracle search on a…, White Noise in Quantum Random Walk Search Algorithm, Quantum random walk search on satisfiability problems, Adjacent Vertices Can Be Hard to Find by Quantum Walks, A random walk approach to quantum algorithms, QUANTUM HITTING TIME ON THE COMPLETE GRAPH, Discrete Quantum Walks and Search Algorithms, Se p 20 06 A random walk approach to quantum algorithms, Finding tree symmetries using continuous-time quantum walk, Journal of Computer and System Sciences 62, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vazirani, in Proceedings of ACM Symposium on Theory of Computing (STOC), By clicking accept or continuing to use the site, you agree to the terms outlined in our. We describe the Grover’s search algorithm and estimate its complexity.

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