Shunyue Yuan

Di Luo, Shunyue Yuan, James Stokes et al.

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.

Chenghan Li, Or Sharir, Shunyue Yuan et al.

Drawing inspiration from the domain of image super-resolution, we view the electron density as a 3D grayscale image and use a convolutional residual network to transform a crude and trivially generated guess of the molecular density into an accurate ground-state quantum mechanical density. We find that this model outperforms all prior density prediction approaches. Because the input is itself a real-space density, the predictions are equivariant to molecular symmetry transformations even though the model is not constructed to be. Due to its simplicity, the model is directly applicable to unseen molecular conformations and chemical elements. We show that fine-tuning on limited new data provides high accuracy even in challenging cases of exotic elements and charge states. Our work suggests new routes to learning real-space physical quantities drawing from the established ideas of image processing.