The newborn Quantum Natural Language Processing (QNLP) field has experienced tremendous growth in recent years. The possibility of applying quantum mechanics to critical aspects of language processing has dramatically impacted many tasks, ranging from theoretical approaches to algorithms implemented on real quantum hardware. From a methodological point of view, the possibility offered by applying quantum mechanics to NLP problems is well suited to classification tasks. This work aims to test the potential computational advantages of a hybrid algorithm, namely the Variational Quantum Classifier (VQC), to perform classification on a classical Linguistics task: acceptability judgments. VQC is a quantum machine learning algorithm able to infer the relations between input features and the associated belonging class using a parametrized quantum circuit and an encoding layer that embeds classical data into quantum states. An acceptability judgment is defined as the ability to determine whether a sentence is considered as natural and well-formed by a native speaker. The approach has been tested on sentences extracted from ItaCoLa, a corpus that collects Italian sentences labeled with their acceptability judgment. The evaluation phase has considered quantitative metrics and qualitative analysis to investigate further the algorithm’s behavior on specific linguistic phenomena included in the corpus.