Study Of The Photon Number Statistics And Quantum Walks On Chips

As the tool of human communication,information plays a vital role in the development of society and civilization.Faced with today's faster and faster pace of life,information is increasingly demanded on transmission speed,capacity and security.In the past several hundred years,classical communication,classical data transmission and classical cryptography based on classical information have attracted human's attention,and provided great convenience for human life and scientific researches.Based on the basic principles of classical physics and probability theory and mathematical statistics,light and circuits are used as tools and platforms to construct today's global communication network.However,as the gradual development of science,it has been found that classical physics can only solve the problem of matter moving at low speed.There are defects in explaining micro-system problems.The development of classical information is gradually slow because of the limitations of classical physics.At the beginning of the twentieth century,through the joint efforts of several scientists,the concept of quantum mechanics was put forward,and the behavior of high-speed particles was scientifically explained,which made human beings have a new cognition of the whole material world.Based on the basic principles of quantum mechanics,quantum information science came true.Through the study of quantum mechanics,it can be found that many branches of classical information theory can find corresponding analogy in quantum information theory,such as classical bits and quantum bits,classical logic gates and quantum logic gates.Scientists have also found that quantum communication and quantum computation contrast with classical communication and classical computation have better performance and security.The researches of quantum information gradually become prosperous.At present,the research on quantum computer has plenty of achievements,but it is still in its infancy.In recent years,the research on quantum computation mainly focuses on the algorithm and designs of structures.In general,the research process of quantum computing experiments can be divided into several aspects,initial state preparation,quantum state transformation,quantum state detection,photon number statistics.In this paper,we study the photon number statistics of quantum states and quantum walk by using the basic principles of quantum mechanics and probability theory and statistics.In the photon number statistics of quantum states,the fidelity and relative entropy are used as measurement tools to compare the performance of different quantum states under different ON/OFF detector arrays.In the field of quantum walk,the boundary conditions of one-dimensional discrete quantum walks and onedimensional continuous quantum walks based on waveguide arrays on chips are studied respectively.There are three innovative achievements in this paper:1.In the detection of quantum states,it is difficult to obtain the photon number distributions without photon number resolution detectors.However,if we divide the quantum state into equal parts,the number of photons of them can be estimated using detector arrays composed of several ON/OFF detectors.In this study,we use this method to estimate the photon number distributions of six common quantum states,and use the fidelity and relative entropy as measurement tools to evaluate the performance of the whole detection system when different quantum states and different parameters of detectors are considered.The results show that the quantum states with discontinuous photon number distribution have large errors when the detector noise is large.For the quantum states with continuous photon number distribution,the photon number can compensate each other when detected,so it is more suitable for this kind of detection method.The results of this study can provide a good theoretical support for the experiments.2.In the study of one-dimensional discrete-time quantum walk,it is usually assumed that the walking area is infinite and not affected by boundary conditions.However,in large-scale quantum circuits,photons inevitably move to the waveguide edge due to the increase of steps.Firstly,the chip structure is designed by using multiple directional couplers to implement multi-step walks and edge waveguides.The boundary conditions of discrete-time quantum walk based on this structure are studied experimentally and theoretically.We obtain the rules of the results of walk changing with waveguide parameters.The research results can help us better understand and characterize discrete-time quantum walk,and provide convenience in related quantum search problems.3.In the study of one-dimensional continuous-time quantum walk based on waveguide coupling structures,the results are usually simulated by using the equation with Bessel functions.However,when the walking distance is too long,the photon will walk to the edge of the waveguide arrays.Unlike discretetime quantum walk,there is no phase difference at the edge of the waveguide arrays.The boundary conditions of continuous-time quantum walk based on multi-waveguide arrays coupled on chips s are studied experimentally and theoretically.In the experiment,the photon number of the walking results is counted by the optical fiber-coupling platform.The results are theoretically simulated with the help of a mirror photon whose phase has a coefficient "i" different with the real photon.The mirror photon is put symmetry relative to the waveguide edge is introduced for simulation.The results of this study can help to calculate and design waveguide structures based on continuous-time quantum walk in dealing with quantum search and quantum maze problems.In summary,through the study of quantum states and boundary conditions of quantum walks,the theoretical calculation methods of photon number statistics under different conditions are given and verified experimentally.Based on the results obtained,it can help to design and calculate the new structures to realize different kinds of quantum algorithm based on quantum walks.