Learning from quantum states: thermal states, ground states, and novel architectures

We present novel methodologies for quantum machine learning (QML) utilizing insights from thermal and ground states. Specifically, we compare the performance of low-temperature thermal states and variational quantum eigensolver (VQE) ground states for QML applications, identifying optimal conditions for each approach. In addition, we introduce new QML architectures inspired by Siamese and twin neural network frameworks. By applying these architectures to specific graph problems and analyzing the spectral properties of graph-derived Hamiltonians, we demonstrate the utility of these approaches in quantum-enhanced graph analysis.