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 ϵ 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.

在可以物理实现量子算法的条件下，将量子算法应用于经典控制系统的状态估计器设计中。我们证明了状态估计器的设计可以通过量子算法来解决，与传统的经典算法相比，量子算法可以实现显着的加速。当系统矩阵稀疏并且条件数κ和精度ϵ的倒数在大小O中较小时，时间复杂度可以从O（n ⁶）减少到O（qn）（poly log（n）），其中n为状态x的维数（t），而q是输入u（t）的维数。我们的研究将提供构造状态估计量的完整量子方案，可以看作是拓宽量子计算应用范围的尝试。