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The prevalence of heart diseases is rising quickly throughout the world, which has an impact on both the world economy and public health. According to the recent statistical survey reports, the increasing mortality rate is due to high blood pressure, high cholesterol, the use of tobacco, obesity, and an inconsistent pulse rate. It is difficult and time-consuming to investigate the various variations of these factors and their impact on Coronary Artery Disease (CAD). Therefore, it is necessary to use modern approaches to diagnose the disease early and minimize the mortality rate. The fields of machine learning and data mining have a wide research dimension and various novel techniques that could help in the prediction of CAD in its early stages and identify their patterns and behaviors in a huge amount of data. The results of such predictions will aid the clinical staff in decision making and early diagnosis. In such a scenario, we proposed a quantum version of the Fully Convolutional Neural Network (FCQ-CNN) for Ischemic Heart Disease (IHD) classification. The proposed model evaluates the quantum circuit-based technique that was inspired by convolutional neural networks, a very successful machine learning model. This method provides $O(log (n))$ depth for $n$ qubits, reducing the number of parameters and allowing for effective training and testing of real quantum devices. The model has been evaluated by considering the IHD dataset after the data has been cleaned and filtered through the Maximally Relevant Minimally Redundancy (MRMR) filter. For dimension reduction, a Support Vector Machine along with Recursive Feature Elimination (SVM-RFE) has been considered. Initially, the model is tested with 20% of the whole dataset and gets the promising results of a testing accuracy of 84.6% with a testing loss of 0.28. By taking into account the same optimal parameters, the proposed model outcomes are compared to those of the classical Optimized Convolution Neural Network (Optimized-CNN) and Fully Connected Neural Network (FCNN) models. Comparing the model’s competency to that of earlier published quantum models yields improvements in accuracy of 8.6%, 12.6%, 3.5%, and 1.8% respectively.