Study On The Properties Of Sacalable Quantum Walks

The combination of quantum mechanics with information science and computer science results in quantum information and quantum computation.Through the unitary evolution of the quantum superposition state,the quantum computation can realize the high parallel computation,thus the exponential acceleration of the classical algorithms can be realized.Quantum algorithms will be widely used in physics,chemistry,biology and economics.It is very difficult to design a good quantum algorithm,however,with the help of quantum randomwalk,more efficient and faster quantum algorithms can be constructed.Quantum random walk also has important applications in quantum state transfer,entanglement generation,and quantum measurements and so on.The properties and physical realization of different types of quantum random walks have been investigated in detail.The properties of quantum random walks can improve the performance of quantum algorithms compared with the algorithms based on classical random walks.This paper mainly investigates the properties and applications of scalable quantum walks.Several quantum algorithms are introduced first.Then the model of one-dimensional and two-dimensional quantum random walk,and the search algorithms and quantum state measurement based on quantum walk are introduced.Through the method of numerical calculation,the properties of the one dimensional asymmetrical quantum walk are discussed.Unbiased quantum walk is counterpart of classical unbiased random walks in the quantum world,and it includs unbiased coin operation and conditional shift operation.Unbiased coin operation changes the probability that a walker walks in different directions.Unbiased conditional shift operation changes the walking distance of the walker to different directions.We describe one dimensional chain of the average properties of scalable quantum walk through the location probability distribution,the probability of walker return to the origin and average location.This paper focuses on whether it has recurrence.Recurrence is an important phenomenon in the evolution of physical systems over time.In quantum walk,because of the the entanglement between the walkers and coins,the complete recovery of the whole system is not possible,only partial recovery can be realized.So the recurrence of quantum walk usually refers to the location of the walker to go back to the initial position.We study the recurrence property of unbiased quantum walks in detail.Numerical calculations show that the recurrence property depends on the unbiased coin operation and conditional shift operation,and does not have relation to the initial coin state and the final distributions.However,the recurrence of classical random walk depends on both the unbiased operations and the final distributions.This is the different property between unbiased quantum walks and classical random walks.The discussion on the properties of unbiased quantum random walks will further promote its applications in simulating the evolution process of virus infection,training complex neural network with recoverable nature,research on complex network transmission efficiency and special algorithm based on complex network.