Quantum-inspired intelligent modeling of radiative magneto-Carreau nanofluid flow with 3D unsteady effects

This research investigates the unsteady three-dimensional radiative flow of a magneto-Carreau nanofluid using the 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 nonlinear ordinary differential equations using similarity transformations. The ODEs 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 behavior 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 artificial neural network using Levenberg–Marquardt showed that the QNN converged faster, had a more accurate mean squared error and regression accuracy. We conclude that the hybrid variational circuit enables the QNN to provide genuine quantum advantage, in part due to the fact that the QNN generalizes more consistently and with greater efficiency than a classical surrogate, thus demonstrating both its novelty in multiphysics nanofluid modeling. Also, the rigorous inferential statistical analysis is also performed for the comparison of QNN with classical neural networks.