Quantum Walk on the Line

By Nayak Ashwin, Vishwanath Ashvin. 2000

136 citations recorded by the source corpus.

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Quantum Walk Based Search Algorithms (2008, background): “Different parameters related to quantum walks and possible speedups of classical algorithms were investigated by several researchers [ 30 ,8,3,29,19,32].”
Search via quantum walk (2006, background): “Afterwards notions related to quantum walks, such as mixing time, and deviation from starting state, were studied for restricted graphs by several researchers [ 22 , 7, 3, 23], suggesting the possibility of speedup of classical algorithms based on random walk.”
A new type of limit theorems for the one-dimensional quantum random walk (2002, background): “Very recently quantum random walks have been widely investigated by a number of groups in connection with the quantum computing, for exmples, [1, 3, 4, 5, 6, 8, 9 , 13, 14].”
QUANTUM WALKS AND THEIR ALGORITHMIC APPLICATIONS (2003, background): “is used. The probability distribution for this coin transformation is shown in figure 2. Two other quantum effects remain for almost any choice of coin transformation and starting state[5, 15 ].”