In the realm of intelligent healthcare, there is a growing ambition to reshape medical services through the integration of artificial intelligence (AI). However, conventional machine learning faces inherent challenges such as privacy issues, delayed updates, and protracted training times, particularly due to the hesitance of medical institutions to directly share sensitive data, with possible noises. In response to these concerns, a Quantum-Assisted Federated Intelligent Diagnosis Algorithm (β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta $$\\end{document}-QuAFIDA) is proposed, applied into real medical data. Leveraging the capabilities of the 5G mobile network, this approach works the connection between Internet of Medical Things (IoMT) devices through the 5G, synchronizing training and updating the server model without disrupting their real-world applications. In our quest to safeguard patient data and enhance training efficiency, our study employs an innovative heuristic approach marked by a nested loop structure. Specifically, the inner loop is dedicated to training the beta-variational quantum eigensolver (β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta $$\\end{document}-VQE) to approximate the expectation values of the proposed algorithm; the outer loop trains the β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta $$\\end{document}-QuAFIDA to reduce the relative entropy towards the target. This approach involves a balance between privacy considerations and the urgency of training. Results demonstrate that representations with low-rank attained through β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta $$\\end{document}-QuAFIDA offer an effective approach for acquiring low-rank states. This research signifies a step forward in the synergy between AI and 5G technologies, presenting a novel avenue for the advancement of intelligent healthcare.