Schizophrenia is a serious chronic mental disorder that significantly affects daily life. Electroencephalography (EEG), a method used to measure mental activities in the brain, is among the techniques employed in the diagnosis of schizophrenia. The symptoms of the disease typically begin in childhood and become more pronounced as one grows older. However, it can be managed with specific treatments. Computer-aided methods can be used to achieve an early diagnosis of this illness. In this study, various machine learning algorithms and the emerging technology of quantum-based machine learning algorithm were used to detect schizophrenia using EEG signals. The principal component analysis (PCA) method was applied to process the obtained data in quantum systems. The data, which were reduced in dimensionality, were transformed into qubit form using various feature maps and provided as input to the Quantum Support Vector Machine (QSVM) algorithm. Thus, the QSVM algorithm was applied using different qubit numbers and different circuits in addition to classical machine learning algorithms. All analyses were conducted in the simulator environment of the IBM Quantum Platform. In the classification of this EEG dataset, it is evident that the QSVM algorithm demonstrated superior performance with a 100% success rate when using Pauli X and Pauli Z feature maps. This study serves as proof that quantum machine learning algorithms can be effectively utilized in the field of healthcare.