Gauge symmetries play a key role in physics appearing in areas such as quantum field theories of the fundamental particles and emergent degrees of freedom in quantum materials. Motivated by the desire to efficiently simulate many-body quantum systems with exact local gauge invariance, gauge equivariant neural-network quantum states are introduced, which exactly satisfy the local Hilbert space constraints necessary for the description of quantum lattice gauge theory with Zd gauge group on different geometries. Focusing on the special case of Z2 gauge group on a periodically identified square lattice, the equivariant architecture is analytically shown to contain the loop-gas solution as a special case. Gauge equivariant neural-network quantum states are used in combination with variational quantum Monte Carlo to obtain compact descriptions of the ground state wavefunction for the Z2 theory away from the exactly solvable limit, and to demonstrate the confining/deconfining phase transition of the Wilson loop order parameter.

翻译：Gauge 的对称性在诸如量子场理论和量子材料自由度的突现度等物理领域中发挥着关键作用。由于希望以精确的本地测量度变化性来高效模拟多体量子系统,因此引入了测量等异性神经网络量子状态,这完全符合Hilbert 与Zd 测量仪组对不同地貌进行量子拉特测量仪理论描述所需的本地空间限制。侧重于Z2 测量仪组在定期识别的平方格上的特例,正方格结构通过分析显示含有循环气溶液,作为特例。高热等等异性神经网络量子状态与变异量量 Monte Carlo 结合使用,以获得关于Z2 理论离完全可溶性极限的地面状态波函数的简明描述,并演示威尔逊循环线参数的定置/分解阶段过渡。