Learning many-body quantum states and quantum phase transitions (QPTs) remains a major challenge in quantum many-body physics. Classical machine-learning methods offer certain advantages in addressing these difficulties. In this paper, we shift the research perspective that bypasses the need for high-fidelity quantum states by directly learning the parameters of parametrized quantum circuits. By integrating attention mechanisms with a variational autoencoder, we efficiently capture hidden correlations within the parameter distribution that encode quantum phase boundaries. These correlations enable us to extract phase transition information in an unsupervised manner and identify a data-driven generalized order parameter from the learned latent space. The framework remains robust even when the variational quantum eigensolver (VQE) converges to local minima rather than true ground states. Moreover, our framework acts as a classical representation of VQE optimization landscapes, enabling the reconstruction of complete phase diagrams. Our results demonstrate that QPT information can indeed be extracted directly from variational circuit parameters.

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• Machine learning
• Quantum circuits
• Quantum phase transitions
• Quantum many-body systems