Modified Quantum Neural Network Enhances Modeling of Nonlinear Dynamic Systems

A Modified Quantum Neural Network framework achieves faster convergence, reduced mean-square error, and improved generalization when modeling nonlinear dynamic systems compared to classical quantum neural network models. Developed as a refined quantum-inspired modeling structure, the enhanced network demonstrated these performance advantages in simulation evaluations conducted across three benchmark nonlinear dynamic systems.

The primary research objective of the framework was not to compete with alternative neural network architectures, but rather to refine and improve the fundamental quantum neural network structure itself. To accomplish this, the architecture introduces targeted structural adjustments at both the input encoding stage and the output processing stage, with all parameters updated through gradient-based learning to maintain stable convergence.

At the input stage, the modified network alters the mechanism used to prepare incoming data. While conventional quantum neural networks apply a sigmoid transformation prior to phase modulation, the modified design maps raw inputs directly into phase values. This direct phase encoding broadens the representational capacity of the hidden-layer quantum neurons, enabling them to capture richer nonlinear phase interactions.

At the output stage, the architecture replaces the traditional trigonometric interference-based output neuron with a trainable amplitude–bias unit. Within this unit, an output scaling coefficient, denoted as C_o, and a bias term, denoted as w_o, are adaptively tuned during learning. This structural change simplifies the output mapping mechanism and enhances the network’s ability to normalize and dynamically scale its output.

The performance of the framework was evaluated across three benchmark nonlinear dynamic systems and compared solely against the classical quantum neural network under identical test conditions. Simulation results confirmed that the modified architecture achieved faster convergence, lower mean-square error, and improved generalization capability across the benchmark systems.

Subject of Research: Quantum neural networks for nonlinear dynamic system modeling

Article Title: An improved Quantum Neural Network with adaptive phase–amplitude processing for nonlinear system modeling

Article References: Kumar, R. (2026). An improved Quantum Neural Network with adaptive phase–amplitude processing for nonlinear system modeling. Quantum Information Processing, 25(11), Article 362. https://doi.org/10.1007/s11128-026-05397-6

Image Credits: AI Generated

DOI: 10.1007/s11128-026-05397-6

Keywords: quantum neural networks, nonlinear dynamic systems, phase encoding, amplitude-bias unit, quantum computing, machine learning, gradient-based learning, system modeling, improved, Quantum, Neural, Network