Quantum Algorithms For System Identification And Control Problems

With the development of quantum physics and computational science,quantum computation aims to break the limit of the traditional calculation and improve computation power based on the characteristics of quantum superposition and parallel processing.Due to the powerful computing capacity in such problems as large integer decomposition,quantum computing is considered to be a new computing model that may have a subversive impact on the future.And it provides new ideas for solving difficult computing problems.As common classical problems,quantum algorithm research on system identification and control problems is of significant meaning.In this thesis,we deeply study quantum algorithms of system identification and control problem under the premise that quantum algorithms can be implemented on quantum computers.The main content is shown as follows:First,we study the application of quantum algorithm in the design of classical state estimators.In order to effectively connect quantum algorithms and improve computational efficiency,we design a quantum states converter.For the classical control system with dimension n,when the system matrix is sparse and the condition number ? and the reciprocal of precision ? are small in size O(poly log(n)),the time complexity of the design of classical state estimators can be reduced from O(n6)to O(qn),where q is the dimension of input u(t).According to the theoretical analysis and simulation,we obtain that when the original system is stable,the quantum measurement error has little effect on the accuracy of state estimation.Second,we propose a quantum scheme for classical system identification problems and analyze the effects of quantum measurement error on the accuracy of system identification.Based on the quantum singular value estimation algorithm,we analyze the structure of the linear regression equation and obtain the simplified quantum scheme.For a discrete system with dimension n,our scheme can reduce the time complexity of the system identification from O((m+n)2N)to O((?)log(N))when both the condition num-ber ? of related matrices and the reciprocal of precision ? are small in size O(poly log(N)),where m is the dimension of the input u and N is the number of samples.Similarly,when the discrete system is stable,the quantum measurement error has little effect on the accuracy of system identification.Third,we study the classical quantum hybrid algorithm for quantum state chromatography.Based on the classical algorithm of quantum state tomography,we propose an entire new scheme.For a quantum system with dimension d,the entire scheme can reduce the time complexity of quantum state tomography from O(d~6)to O(K3d/?)when both the condition number ? of related matrices and the reciprocal of precision ? are O(poly log d).The scheme achieves significant acceleration,and reduces the cost of quantum algorithms on computing resources as much as possible.Finally,we summary our work in this dissertation and suggest possible investigations for future improvement and perfection on our research.