System Identification Methods For Typical Quantum Systems With Projective Measurements

With the development of science and technology in quantum computation andquantum information, it becomes more possible to control quantum phenomenon, sohow to build and identify quantum mechanic systems becomes more and moreimportant. Because of the quantum features which do not exist in classic systems, thereare many differences between the identification on quantum systems and classicsystems; therefore it is worthy to specially investigate the quantum system identification.However, due to the extensive fields and complexity of identification, systematicalresearch findings are rarely reported. For this sake, in the thesis, we proposed newapproaches of system identification for three typical quantum systems with projectivemeasurements. The main contents are summarized as follows:(1) We demonstrated in details the Bloch sphere geometric representation ofquantum state, system evolution and projective measurement, and illustrated the basicpostulates in quantum mechanics in a geometric way.(2) We designed the computer simulation procedure for quantum systemidentification, including how to simulate the evolution process of the identificationobject by using the Bloch vector evolution equation, and how to simulate the practicalexecutive course of the projective measurements.(3) We proposed the system identification methods for three typical quantumsystems i.e. hydrogen-like atomic spontaneous emission system, two-qubit spin chainsystem and single photon linear optical system. We described the method from threeangles, which were the selection of model sets and parameters, the generation of datafor identification and the application of the criterion, and paid great attention to theconnection between data and parameters.(4) Due to the high cost of physical experiments on quantum systems, we tesifiedthe identification methods by using computer simulation. The models and parameters ofsimulation were set by the standard of physical process in the approximate reality; thedata for identification were generated through computer simulation of the evolution ofthe identification objects and the practical executive operation of projectivemeasurements; the criterion were selected from classic identification critira based on thefeatures of models and data.(5) We analysed the factors affecting identification accuracy. Starting with thecourse of obtaining identification data, existing classic errors, we investigated theeffects of operation errors during projective measurements on system states reflected bythe obtained data, summarized the matching relation between the discrete samplingmethod and the model expression of the system state, and analysed identificationaccuracy of the proposed identification methods by using simulation while these classic errors existed.After reviewing the main developments in quantum system identification, combining the existing results and making full use of the features of quantum states and projective measurements, we proposed a new approach of parameter estimation for typical quantum systems through the connection between the model parameters characterizing the quantum system evolution and the data reflecting the information of quantum system states, and tesified the feasibility through simulation examples, moreover analysed the factors affecting the identification accuracy. The main work and contributions of this thesis can promote the studies of the quantum system identification.