Gauge theories appear broadly in physics, ranging from the standard model of particle physics to long-wavelength descriptions of topological systems in condensed matter. However, systems with sign problems are largely inaccessible to classical computations and also beyond the current limitations of digital quantum hardware. In this work, we develop an analog approach to simulating gauge theories with an experimental setup that employs dipolar spins (molecules or Rydberg atoms). We consider molecules fixed in space and interacting through dipole-dipole interactions, avoiding the need for itinerant degrees of freedom. Each molecule represents either a site or gauge degree of freedom, and Gauss's law is preserved by a direct and programmatic tuning of positions and internal state energies. This approach can be regarded as a form of analog systems programming and charts a path forward for near-term quantum simulation. As a first step, we numerically validate this scheme in a small-system study of $\mathrm{U}\left(1\right)$ quantum link models in ($1+1$) dimensions with link spin $S=1/2$ and $S=1$ and illustrate how dynamical phenomena such as string inversion and string breaking could be observed in near-term experiments. Our work brings together methods from atomic and molecular physics, condensed matter physics, high-energy physics, and quantum information science for the study of nonperturbative processes in gauge theories.

中文翻译：

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用偶极自旋系统模拟量规理论的框架

规范理论在物理学中广泛出现，从粒子物理学的标准模型到凝聚态拓扑系统的长波描述。但是，带有符号问题的系统在很大程度上无法进行经典计算，而且也超出了数字量子硬件的当前限制。在这项工作中，我们开发了一种模拟方法，可通过使用偶极自旋（分子或里德堡原子）的实验装置来模拟量规理论。我们认为分子固定在空间中并通过偶极-偶极相互作用相互作用，从而避免了对迭代自由度的需求。每个分子代表一个位点或一个规范的自由度，高斯定律通过位置和内部状态能量的直接和程序调整来保持。这种方法可以被视为模拟系统编程的一种形式，并为近期量子模拟指明了前进的道路。第一步，我们在一个小型系统研究中对该方案进行了数值验证$\mathrm{ü}（\mathrm{1个}）$ （中的量子链接模型$\mathrm{1个}+\mathrm{1个}$）链接旋转的尺寸 $\mathrm{小号}=\mathrm{1个}/2$ 和 $\mathrm{小号}=\mathrm{1个}$并说明了如何在近期实验中观察到诸如弦反转和弦断裂之类的动力学现象。我们的工作汇集了原子和分子物理学，凝聚态物理学，高能物理学和量子信息科学等方法，用于规范理论中的非摄动过程研究。