Unified quantum state tomography and Hamiltonian learning: A language-translation-like approach for quantum systems

As quantum technology rapidly advances, the need for efficient scalable methods to characterize quantum systems intensifies. Quantum state tomography and Hamiltonian learning are essential for interpreting and optimizing quantum systems, yet a unified approach remains elusive. Such an integration could enhance our understanding of the complex relationship between quantum states and Hamiltonians, contributing to the development of more efficient methodologies. In this paper, we present a method that integrates quantum state tomography and Hamiltonian learning, drawing inspiration from machine translation in the field of natural language processing (NLP). We demonstrate the effectiveness of our approach across a variety of quantum systems, successfully learning the complex relationships between quantum states and Hamiltonians. Furthermore, the scalability and few-shot learning capabilities of our method could potentially minimize the resources required for characterizing and optimizing quantum systems. Our research provides valuable insights into the relationship between quantum states and Hamiltonians, paving the way for further studies on quantum systems and advancing quantum computation and related technologies.