Research On Properties Of Quantum Walks And The High Dimensional Quantum State Transition

Quantum walk is the counterpart of classical random walk in the quantum world.Because of the coherent superposition and quantum interference,the algorithm based on quantum walk has better performance and efficiency than classical random walk.In addition,quantum walk is widely used in quantum communication and quantum simulation.In this paper,we mainly discuss the basic properties of discrete-time quantum walks,and introduce quantum control operations to achieve the coherent superposition of different properties of walks.The programmable quantum walk,which can precisely control the high-dimensional quantum state,is achieved through an optical loop structure.The main work is summarized below.The study on the transition between quantum walk and classical random walk is helpful to understand the computational properties of quantum walk and the dynamics associated with these two walks.Existing research has achieved mixed states of different types of walk through decoherence,measurement,and so on.We introduce quantum control to achieve the coherent superposition states of two types of walks.Through the interaction between the auxiliary bits and the coin walker,the coin-walker evolves to operate the auxiliary bits differently,and realizes the continuous control between the wave state and the particle state in the quantum walk,and prepares the coherent superposition states of the multipath wave and particle states.The position distribution and variance with system coefficients are calculated respectively.The results show that quantum control enables walkers to be in not only the mixed state of particles and waves,but also the coherent superposition state.The differences between the mixed state and the coherent superposition state are given.Our scheme can achieve continuous control between different types of walk through two different ways,coherence and mixing.The high-dimensional coherent superposition state is an important resource in the field of quantum information science and technology.Coin operations that vary with time and space enhance the manipulation of dynamic processes to achieve arbitrary high-dimensional coherent superposition states.However,this experimental implementation of space-and time-nonuniform quantum walk requires stable and precise coin operations,which has not yet been implemented in any system.We use an optical loop structure to achieve nonuniform quantum walk.A stable polarized Sagnac interferometer was used to perform time-and position-dependent coin operations.Combined with different initial state preparation,inhomogeneous quantum walk can simulate the rich dynamic characteristics of single photon,and achieve coherent superposition states of different position states.We have implemented Hadamard,Gaussian,and Coherent uniform distributions respectively,and experimentally verified that the entire evolution process maintains good coherence.Finally,the Shannon entropy is used to measure the randomness of the high-dimensional coherent superposition state.The results show that the randomness increases significantly with the increase of the evolution step t,and the randomness of the coherent uniform distribution is the largest one among these three distributions.The coherent uniform distribution after a quantum measurement directly generates multibit random sequences,and the bit rate can be effectively increased by increasing the evolution step t.