Alzheimer's disease (AD) is a severe neurological disorder that leads to irreversible memory loss. In the previous research, the early-stage Alzheimer's often presents with subtle memory issues that are difficult to differentiate from normal age-related changes. This research designed a novel detection model called the Zeiler and Fergus Quantum Dilated Convolutional Neural Network (ZF-QDCNN) for AD detection using Magnetic Resonance Imaging (MRI). Initially, the input MRI images are taken from a specific dataset, which is pre-processed using a Gaussian filter. Then, the brain area segmentation is performed by utilizing the Channel-wise Feature Pyramid Network for Medicine (CFPNet-M). After segmentation, relevant features are extracted, and the classification of AD is performed using the ZF-QDCNN, which is the integration of the Zeiler and Fergus Network (ZFNet) with the Quantum Dilated Convolutional Neural Network (QDCNN). Moreover, the ZF-QDCNN model demonstrated promising performance, achieving an accuracy of 91.7%, a sensitivity of 90.7%, a specificity of 92.7%, and a f-measure of 91.8% in detecting AD. Additionally, the proposed ZF-QDCNN model effectively identifies and classifies Alzheimer's disease in MRI images, highlighting its potential as a valuable tool for early diagnosis and management of the condition.