As science and technology advance, industrial manufacturing processes get more complicated. Back Propagation Neural Network (BPNN) convergence is comparatively slower for processing nonlinear systems. The nonlinear system used in this study to evaluate the optimization of BPNN based on the LM algorithm proved the algorithm’s efficacy through a MATLAB simulation analysis. This paper examined the application impact of the enhanced approach using the Continuous stirred tank reactor (CSTR) control system as an example. The study’s findings demonstrate that the LM optimization algorithm’s identification error exceeds 10-5. The research’s suggested control approach for reactant concentration CA in CSTR systems provides a better tracking effect and a stronger anti-interference capacity. Compared to the PI control method, the overall control effect is superior. As a result, the optimization model for nonlinear systems has a greatly improved processing accuracy. With some data support for the accuracy study of neural network models and the application of nonlinear systems, the suggested LM-BP optimization algorithm is evidently more appropriate for nonlinear systems.

Quantum key agreement is an important topic that the shared key must be negotiated equally by all participants, and any nontrivial subset of participants cannot fully determine the shared key. To date, the embed modes of subkey in all the previously proposed quantum key agreement protocols are based on either BB84 or entangled states. The research of the quantum key agreement protocol based on quantum search algorithms is still blank. In this paper, on the basis of investigating the properties of quantum search algorithms, we propose the first quantum key agreement protocol whose embed mode of subkey is based on a quantum search algorithm known as Grover’s algorithm. A novel example of protocols with 5 – party is presented. The efficiency analysis shows that our protocol is prior to existing MQKA protocols. Furthermore it is secure against both external attack and internal attacks.