在应用导向下注重研究不同量子子系统之间关联、量子系统与各种环境相互作用、不同典型相互作用类型影响、量子测量产生信息丢失所导致的量子系统的复杂性问题，也考虑量子多体系统与多物理参数所引入的量子系统的复杂性问题。力图从动力学求解和物理量计算的方法与理论的研究入手，进而寻求并得到应用中有兴趣有意义问题的解决方案。本课题拟使用张量网络算法，也会采用密度矩阵重整化群与泛函重整化群算法研究复杂的强关联系统；并研究复杂的关联环境对quantum metrology 的影响，分析精度的极限及相关问题等,以获知在复杂环境下复合量子系统中如何控制和影响其物理性质的理论机制与实验方案。同时，将主要使用我们改进的与加条件的两体密度矩阵变分法，并参照量子蒙特卡罗方法研究多维多自由度系统，重点目标在于提高计算效率与精度。此外，量子失协与量子关联动力学以及经典复杂系统对量子复杂系统推广的几个问题也会在本课题

According to the application orientation, we mainly research the quantum system complexities that come from the correlations among the quantum subsystems, the interactions between quantum system and environments, the influences of various kinds of typical interactons, and information loss via quantum measurements, we also stydy those complexities that are introduced by the many-body quantum systems and many physical parameters. Try to process from the investigation of methods and theory about dynamics solutions and physical quantity calculations in the complex quantum systems, we expect to seek and then obtain the solution programes for significant and interesting problems of applications. In this project, we will use the tensor network state-based algorithm, as well as the density matrix renormalization group and the functional renomornization group algorithms to research the complexity of strongly correlated systems. We study the influence and effection on quantum metrology from the complex environments, and analysis the precision bound and related problems in order to obtian the knowledge about the theoretical mechanisms and experimental schemes how to control their physical properties. At the same time, we mainly use our improved and conditional various methods of two-body density matrix, also consult with quantum Monte Carlo method to research the many-body quantum systems so that the efficiency and precision of relvant calculations are advanced. In addition, the dynamics of quantum discord and quantum entanglement, as well as the some scientific problemes in the extensions from the complex classical systems to complex quantum systems will be included into this research.