论文标题
2+1d U（1）量规的神经网络（1）量规理论模拟在哈密顿公式中
Gauge Equivariant Neural Networks for 2+1D U(1) Gauge Theory Simulations in Hamiltonian Formulation
论文作者
论文摘要
量规理论在许多领域的科学领域都起着至关重要的作用，包括高能量物理，凝结物理学和量子信息科学。在晶格仪理论的量子模拟中，一个重要的步骤是构建遵守量规对称性的波函数。在本文中，我们开发了量规模拟的神经网络波函数技术，用于模拟哈密顿公式中的连续变化量子晶格量规。我们已经应用了量规的神经网络方法，以使用变异蒙特卡洛（Monte Carlo）使用U（1）量规组找到2+1维晶格仪理论的基态。我们已经针对最先进的复杂高斯波函数进行了基准测试，这表明在强耦合方案中的性能提高了，并且在弱耦合方案中的可比结果。
Gauge Theory plays a crucial role in many areas in science, including high energy physics, condensed matter physics and quantum information science. In quantum simulations of lattice gauge theory, an important step is to construct a wave function that obeys gauge symmetry. In this paper, we have developed gauge equivariant neural network wave function techniques for simulating continuous-variable quantum lattice gauge theories in the Hamiltonian formulation. We have applied the gauge equivariant neural network approach to find the ground state of 2+1-dimensional lattice gauge theory with U(1) gauge group using variational Monte Carlo. We have benchmarked our approach against the state-of-the-art complex Gaussian wave functions, demonstrating improved performance in the strong coupling regime and comparable results in the weak coupling regime.
