The design of quantum many body systems, which have to fulfill an extensive number of constraints, appears as a formidable challenge within the field of quantum simulation. Lattice gauge theories are a particular important class of quantum systems with an extensive number of local constraints and play a central role in high energy physics, condensed matter and quantum information. Whereas recent experimental progress points towards the feasibility of large-scale quantum simulation of Abelian gauge theories, the quantum simulation of non-Abelian gauge theories appears still elusive. In this paper we present minimal non-Abelian lattice gauge theories, whereby we introduce the necessary formalism in well-known Abelian gauge theories, such as the Jaynes-Cumming model. In particular, we show that certain minimal non-Abelian lattice gauge theories can be mapped to three or four level systems, for which the design of a quantum simulator is standard with current technologies. Further we give an upper bound for the Hilbert space dimension of a one dimensional SU(2) lattice gauge theory, and argue that the implementation with current digital quantum computer appears feasible.

中文翻译：

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从杰恩斯-卡明斯模型到非阿贝尔规范理论：量子工程师导览

量子多体系统的设计必须满足大量约束，这在量子模拟领域似乎是一项艰巨的挑战。格子规范理论是一类特别重要的量子系统，具有大量局部约束，在高能物理学、凝聚态物质和量子信息中发挥着核心作用。尽管最近的实验进展表明阿贝尔规范理论的大规模量子模拟的可行性，但非阿贝尔规范理论的量子模拟似乎仍然难以捉摸。在本文中，我们提出了最小的非阿贝尔格规范理论，由此我们引入了著名的阿贝尔规范理论（例如 Jaynes-Cumming 模型）中的必要形式。特别是，我们展示了某些最小非阿贝尔格子规范理论可以映射到三级或四级系统，为此量子模拟器的设计是当前技术的标准。此外，我们给出了一维 SU(2) 格子规范理论的希尔伯特空间维数的上限，并认为用当前的数字量子计算机实现似乎是可行的。