Research On Realizing Arbitrary Distribution Based On Programmable Quantum Walk

Quantum information is a new information processing method based on quantum mechanics,which calculates,encodes and transmits information on the physical information contained in a quantum system.Quantum information can break through the physical limits of classical information processing and realize brand-new information processing methods.The corresponding model of classical random walk is quantum walk in the quantum world.Compared with the classical random walk,the diffusion rate of quantum walk exhibits a second increase due to quantum coherence.Based on the non-uniform quantum walk in time and space,the coherent superposition of the position states in the quantum walk can be precisely designed to achieve the required unitary evolution,thereby meeting the needs of quantum information applications.The inherent uncertainty in the coherent uniform distribution of quantum walks is used to generate multi-bit true random numbers.This thesis mainly discusses the research of randomness in quantum walks and the experimental realization of arbitrary distribution based on programmable quantum walks.The following two aspects are mainly done.(1)First of all,we theoretically discuss the input single-bit quantum state,based on the evolution process of quantum walk,prepare a multi-path coherent superposition state,and obtain a multi-bit random number through a quantum measurement of the path.We calculated the influence of the input state in detail,the precisely regulated evolution process,and the number of evolution steps on the randomness of the multi-bit quantum pure state.By calculating the Shannon entropy and the minimum entropy,in order to measure the randomness in the quantum walk.For the current single-photon detection technology,the evolution of quantum walks provides a way to increase the rate of random number generation.The innovation is the first to explore the influence of the superimposed relative position of the input initial state on the randomness of the walker.Choosing the appropriate relative phase can effectively improve the randomness of the walker.(2)Secondly,the experiment realized a non-uniform quantum walk in time and space.Through the precise design of the coherent superposition of the position state in the quantum walk,and the operation of different coins,the required unitary evolution can be realized,so as to meet the needs of quantum information applications.We experimentally demonstrate that the rich dynamics,which generate arbitrary distributions such as uniform and Gaussian,can be reached by introducing different sets of the time-and position-dependent coin operations.Moreover,uniform superposition is a robust W entangled state,which has a wide range of applications,such as generating true multi-bit random numbers without post-processing.Such a quantum walk is realized by a resource-saving optical loop,wherein the variable coin operation is executed based on a Sagnac interferometer in an intrinsically stable and precisely controlled way.Our results contribute to the practical realization of quantum computation,quantum simulations and quantum information protocols.