Purpose: The research proposes a quantum-mathematical intelligent computing method to model and optimize heat conduction and chemically reactive transport of three-dimensional Carreau fluid flow (HCRCP-CFF). The goal is to define a precise and effective model for describing nonlinear thermal and rheological properties of complex fluids applicable in industrial, chemical and biomedical processes. Design/methodology/approach: The nonlinear governing partial differential equations for heat and reactive mass transport in HCRCP-CFF are simplified to an ordinary differential equation system and solved numerically by MATLAB’s bvp4c solver. The resulting dataset is applied to train a Quantum Neural Network (QNN) with a supervised backpropagation strategy incorporating quantum-inspired operators for faster convergence and learning accuracy. Findings: The QNN model correctly replicates velocity, temperature and concentration profiles with mean squared error values ranging as low as 10−9. Parametric analysis indicates that an increase in Weissenberg number increases the elasticity of flow, whereas the rise in Prandtl number reduces thermal diffusion. The QNN gains robust generalization ability and reduced computational surpasses the existing and numerical schemes in accuracy and convergence. Originality/value: The current research represents the first effort to employ QNNs within a 3D heat-conducting and reactive Carreau fluid interaction system (HCRCP-CFF). What sets this research apart from previous work is that a quantum-enhanced surrogate solver has been developed and shown to outperform all current ANN-based and numerical methods for predicting nonlinear thermorheological interactions, both in terms of accuracy and computational efficiency and having greater generalization ability. The approach also produces completely new types of predictive models for intricate multiphysical flow processes and ultimately can serve as a basis upon which to build next-generation quantum-enhanced intelligent fluid simulation methodologies.