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Schr\"odinger's equation serves as a fundamental component in characterizingquantum systems, wherein both quantum state tomography and Hamiltonian learningare instrumental in comprehending and interpreting quantum systems. Whilenumerous techniques exist for carrying out state tomography and learningHamiltonians individually, no method has been developed to combine these twoaspects. In this study, we introduce a new approach that employs the attentionmechanism in transformer models to effectively merge quantum state tomographyand Hamiltonian learning. By carefully choosing and preparing the trainingdata, our method integrates both tasks without altering the model'sarchitecture, allowing the model to effectively learn the intricaterelationships between quantum states and Hamiltonian. We also demonstrate theeffectiveness of our approach across various quantum systems, ranging fromsimple 2-qubit cases to more involved 2D antiferromagnetic Heisenbergstructures. The data collection process is streamlined, as it only necessitatesa one-way generation process beginning with state tomography. Furthermore, thescalability and few-shot learning capabilities of our method could potentiallyminimize the resources required for characterizing and optimizing quantumsystems. Our research provides valuable insights into the relationship betweenHamiltonian structure and quantum system behavior, fostering opportunities foradditional studies on quantum systems and the advancement of quantumcomputation and associated technologies.

Unified Quantum State Tomography and Hamiltonian Learning Using Transformer Models: A Language-Translation-Like Approach for Quantum Systems