Removal of miscible hazardous materials from aqueous solutions is an alarming problem for the environmental scientists. Several linear and nonlinear regression models like Langmuir, Freundlich, D–R, Tempkin isotherm models are in vogue for determining the adsorbing capacity of standard adsorbents used for this purpose. In this article, we propose a novel quantum inspired backpropagation multilayer perceptron (QBMLP) based on quantum gates (single qubit rotation gates and two qubit controlled-not gates) for the prediction of this adsorption behavior exhibited by calcareous soil oftentimes used in adsorbing miscible iron from aqueous solutions. The backpropagation learning formulae for the proposed QBMLP architecture has also been generalized for multiple number of layers in both field homogeneous and field heterogeneous configurations characterized by three standard activations, viz., sigmoid, tanh and tan1.5h functions. Applications of the efficiency of the proposed QBMLP over the regression models are demonstrated with regards to the prediction behavior of the adsorption of iron by calcareous soil from an aqueous solution with effect to various characteristic adsorbent parameters. The adsorption process is considered to be a physical one since the activation energy (E A ) of ferrous ion adsorption is 9.469kJmol−1 due to Arrhenius. Moreover, the thermodynamic parameters of Gibb's free energy (G 0), enthalpy (H 0) and entropy (S 0) values indicate it be spontaneous. Results indicate that QBMLP predicts the adsorption behavior of calcareous soil to a very closer extent thereby obviating the need for further regression/experimental analysis. Comparison with the performance of a similar classical multilayer perceptron (MLP) architecture also reveals the prediction and time efficiency of the proposed QBMLP architecture. 
A quantum backpropagation multilayer perceptron (QBMLP) for predicting iron adsorption capacity of calcareous soil from aqueous solution