There has been a growing interest in artificial neural networks (ANNs) based on quantum theoretical concepts and techniques due to cognitive science and computer science aspects. The so called Quantum Neural Networks (QNNs) are an exciting area of research in the field of quantum computation and quantum information. We proposed a modeling of Proportional integral derivative neural networks based on quantum computation called QNNs-PID that maps a nonlinear function. We analyze the main algorithms and architecture proposed the modeling of QNNs-PID. The main conclusion is that, up to now, we prove the feed back and back forward algorithm based on quantum computation how to use and give clearly the results for the nonlinear function in the context of QNNs-PID. We simulate an example to show the property of QNNs-PID in nonlinear systems.