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In the realm of liver transplantation, accurately determining hepatic steatosis levels is crucial. Recognizing the essential need for improved diagnostic precision, particularly for optimizing diagnosis time by swiftly handling easy-to-solve cases and allowing the expert time to focus on more complex cases, this study aims to develop cutting-edge algorithms that enhance the classification of liver biopsy images. Additionally, the challenge of maintaining data privacy arises when creating automated algorithmic solutions, as sharing patient data between hospitals is restricted, further complicating the development and validation process. This research tackles diagnostic accuracy by leveraging novel techniques from the rapidly evolving field of quantum machine learning, known for their superior generalization abilities. Concurrently, it addresses privacy concerns through the implementation of privacy-conscious collaborative machine learning with federated learning. We introduce a hybrid quantum neural network model that leverages real-world clinical data to assess non-alcoholic liver steatosis accurately. This model achieves an image classification accuracy of 97%, surpassing traditional methods by 1.8%. Moreover, by employing a federated learning approach that allows data from different clients to be shared while ensuring privacy, we maintain an accuracy rate exceeding 90%. This initiative marks a significant step towards a scalable, collaborative, efficient, and dependable computational framework that aids clinical pathologists in their daily diagnostic tasks.