非阿贝尔格拉菲理论在多维空间中的高效有限资源表述
An efficient finite-resource formulation of non-Abelian lattice gauge theories beyond one dimension
AI总结：
本文提出了一种高效方法，用于在多维空间中计算非阿贝尔规范理论的耦合运行，利用局部基底减少截断误差，扩展了量子计算的应用范围。
摘要：
非阿贝尔规范理论提供了对基本相互作用最准确的描述，在宇宙学和粒子物理学中与实验数据有显著的一致性。使用标准技术可以在连续和格点框架中做出高度精确的预测。然而，经典方法在尝试从格点规范理论研究中推导出连续极限时存在局限性。补充经典计算或结合量子计算方法，以利用当前量子资源改进预测连续极限的准确性，是一个严峻的开放挑战。在本文中，我们提出了一种资源高效的计算方法，用于计算非阿贝尔规范理论在多维空间中的耦合运行。我们首先将周期性格点上的哈密顿量表示为环变量和共轭环电场，利用高斯定律保留与规范无关的项。然后，我们识别出一种局部基底，用于小和大环的变化，以在计算耦合运行时最小化截断误差。我们的方法使当前量子计算机、模拟器和张量网络计算能够在以往无法触及的范围内进行计算。
英文摘要：
Non-Abelian gauge theories provide the most accurate description of fundamental interactions, showing remarkable agreement with experimental data in cosmology and particle physics. Highly precise predictions can be made using standard techniques, both in the continuum and in the lattice frameworks. However, classical methods have limitations, particularly when attempting to extrapolate the continuum limit from the study of lattice gauge theories. Complementing classical computations or combining them with quantum computational methods, to improve the predictions towards the continuum limit with current quantum resources, is a formidable open challenge. In this paper, we propose a resource-efficient method to compute the running of the coupling in non-Abelian gauge theories beyond one spatial dimension. We first represent the Hamiltonian on periodic lattices in terms of loop variables and conjugate loop electric fields, exploiting the Gauss law to retain the gauge-independent ones. Then, we identify a local basis for small and large loops variationally to minimize the truncation error while computing the running of the coupling on small tori. Our method enables computations at arbitrary values of the bare coupling and lattice spacing with current quantum computers, simulators and tensor-network calculations, in regimes otherwise inaccessible.
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