Quantum many-body systems exhibit an extremely diverse range of phases and physical phenomena. However, we prove that the entire physics of any quantum many-body system can be replicated by certain simple, “universal” spin-lattice models. We first characterize precisely what it means for one quantum system to simulate the entire physics of another. We then fully classify the simulation power of all two-qubit interactions, thereby proving that certain simple models can simulate all others, and hence are universal. Our results put the practical field of analogue Hamiltonian simulation on a rigorous footing and take a step toward justifying why error correction may not be required for this application of quantum information technology.

量子多体系统展现出极为多样的相和物理现象。但是，我们证明，任何量子多体系统的整个物理学都可以通过某些简单的“通用”自旋晶格模型来复制。我们首先精确地描述一个量子系统模拟另一个量子系统的整个物理过程意味着什么。然后，我们将所有两个qubit交互的仿真能力完全分类，从而证明某些简单模型可以仿真所有其他模型，因此是通用的。我们的结果将模拟汉密尔顿模拟的实际领域置于一个严格的基础上，并朝着证明为什么量子信息技术的这种应用可能不需要纠错的方向迈出了一步。