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

As quantum technology continues to make rapid strides, the quest for efficient, scalable tools for quantum system characterization assumes greater importance. Quantum State Tomography and Hamiltonian learning have become indispensable for deciphering and fine-tuning quantum systems. The amalgamation of these tools, however, is yet to be realized. Here, we introduce a novel method that facilitates this integration, drawing on the principles of machine translation from the Natural Language Processing (NLP) domain. We apply our methodology to an extensive spectrum of quantum systems, ranging from 2-qubit cases to 2D antiferromagnetic Heisenberg model, and demonstrate the versatility of our approach by employing various Quantum State Tomography methods. Additionally, the scalability of our method, along with its few-shot learning capabilities, promises a significant reduction in the resources needed for quantum system characterization and optimization.