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Effective feature selection is essential for enhancing the performance of artificial intelligence models. It involves identifying feature combinations that optimize a given metric, but this is a challenging task due to the problem's exponential time complexity. In this study, we present an innovative heuristic called Evolutionary Quantum Feature Selection (EQFS) that employs the Quantum Circuit Evolution (QCE) algorithm. Our approach harnesses the unique capabilities of QCE, which utilizes shallow depth circuits to generate sparse probability distributions. Our computational experiments demonstrate that EQFS can identify good feature combinations with quadratic scaling in the number of features. To evaluate EQFS's performance, we counted the number of times a given classical model assesses the cost function for a specific metric, as a function of the number of generations.

Quantum supervised learning, utilizing variational circuits, stands out as a promising technology for NISQ devices due to its efficiency in hardware resource utilization during the creation of quantum feature maps and the implementation of hardware-efficient ansatz with trainable parameters. Despite these advantages, the training of quantum models encounters challenges, notably the barren plateau phenomenon, leading to stagnation in learning during optimization iterations. This study proposes an innovative approach: an evolutionary-enhanced ansatz-free supervised learning model. In contrast to parametrized circuits, our model employs circuits with variable topology that evolves through an elitist method, mitigating the barren plateau issue. Additionally, we introduce a novel concept, the superposition of multi-hot encodings, facilitating the treatment of multi-classification problems. Our framework successfully avoids barren plateaus, resulting in enhanced model accuracy. Comparative analysis with variational quantum classifiers from the technology's state-of-the-art reveal a substantial improvement in training efficiency and precision. Furthermore, we conduct tests on a challenging dataset class, traditionally problematic for conventional kernel machines, demonstrating a potential alternative path for achieving quantum advantage in supervised learning for NISQ era.