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In this paper,quantum algorithms are applied to the design of state estimators in classical control systems under the condition that quantum algorithms can be physically implemented.We demonstrate that the design of state estimators can be solved by quantum algorithms,which may achieve significant acceleration in comparison to traditional classical algorithms.The time complexity can be reduced from O(n6) to O(qn) when the system matrix is sparse and the condition number κ and the reciprocal of precision e are small in size O(poly log(n)),where n is the dimension of state x(t) and q is the dimension of input u(t).Our research will provide an entire quantum scheme of constructing state estimators and can be regarded as an attempt to widen application scope of quantum computation.