Deep neural networks are powerful and flexible models that have gained the attention of the machine learning community over the last decade. Usually, an expert spends significant time designing the neural architecture, with long trial and error sessions to reach good and relevant results. Because of the manual process, there is a greater interest in Neural Architecture Search (NAS), which is an automated method of architectural search in neural networks. NAS is a subarea of Automated Machine Learning (AutoML) and is an essential step towards automating machine learning methods. It is a technique that aims to automate the construction process of a neural network architecture. This technique is defined by the search space aspects of the architectures, search strategy and performance estimation strategy. Quantum-inspired evolutionary algorithms present promising results regarding faster convergence when compared to other solutions with restricted search space and high computational costs. In this work, we enhance Q-NAS: a quantum-inspired algorithm to search for deep networks by assembling simple substructures. Q-NAS can also evolve some numerical hyperparameters, which is a first step in the direction of complete automation. Our contribution involves experimenting other types of optimizers in the algorithm and make an indepth study of the Q-NAS parameters. Additionally, we present Q-NAS results, evolved from scratch, on the CIFAR-100 dataset using only 18 GPU/days. We were able to achieve an accuracy of 76.40% which is a competitive result regarding other works in literature. Finally, we also present the enhanced QNAS applied to a case study for COVID-19 x Healthy classification on a real chest computed tomography database. In 9 GPU/days we were able to achieve an accuracy of 99.44% using less than 1000 samples for training data. This accuracy overcame benchmark networks such as ResNet, GoogleLeNet and VGG.