<![CDATA[The study of topological phase transitions in many-body quantum systems has gained significant attention due to its implications for quantum computing and condensed matter physics. Traditional methods of classifying topological phases often rely on computationally expensive techniques or labeled data, which can be impractical for large systems. This research aims to develop a novel, scalable approach for unsupervised classification of topological phase transitions using Variational Quantum Eigensolvers (VQEs) in conjunction with unsupervised machine learning algorithms. The objective is to efficiently classify quantum phases without requiring pre-labeled data, offering a more efficient solution for studying large, interacting quantum systems. The methodology involves simulating quantum systems, including a 1D spin chain and a 2D topological insulator, and optimizing their ground states using VQEs. Key quantum features, such as energy spectra and correlation functions, are extracted and fed into clustering algorithms to identify different topological phases. The performance of the unsupervised learning algorithm is evaluated through clustering purity and accuracy metrics. The results demonstrate that the proposed method successfully identifies trivial and non-trivial phases with high accuracy (95% for the 1D spin chain and 92% for the 2D topological insulator). ]]>
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