This research investigates the unsteady three-dimensional in the radiative flow of a Magneto-Carreau nanofluid using effects of Brownian motion and thermophoresis on a convectively heated surface. The previous complicated nonlinear system is modeled via a Quantum Neural Network (QNN) model using the Levenberg–Marquardt Algorithm (LMA). The governing partial differential equations are first transformed into a nonlinear ordinary differential equations using similarity transformations. The ODE's were solved numerically using the Adams method to create a reference dataset to train and validate the QNN. The QNN model was implemented in MATLAB using the quantum-inspired parallelism of the QNN to capture the behaviour of fluid dynamics and its advantageous generalization properties. Statistical analyses proved the QNN-LMA technique had a high accuracy and stability. The QNN used a four-qubit amplitude-encoded variational circuit with rotation and entanglement. The comparison of results to a similar ANN using Levenberg-Marquardt showed that the QNN converged faster, mean squared error more accurate, and regression accuracy. We conclude that the hybrid variational circuit enables the QNN to provide genuine quantum advantage, in part due to that the QNN generalizes more consistently and with greater efficiency than a classical surrogate, thus demonstrating both its novelty to multiphysics nanofluid modeling. Also, the rigorous inferential statistical analysis are also performed for the comparison of QNN with classical neural networks.
Abbasi et al. (2026) studied this question.