Quantum Monte Carlo coupled with neural network wavefunctions has shown
success in computing ground states of quantum many-body systems. Existing
optimization approaches compute the energy by sampling local energy from an
explicit probability distribution given by the wavefunction. In this work, we
provide a new optimization framework for obtaining properties of quantum
many-body ground states using score-based neural networks. Our new framework
does not require explicit probability distribution and performs the sampling
via Langevin dynamics. Our method is based on the key observation that the
local energy is directly related to scores, defined as the gradient of the
logarithmic wavefunction. Inspired by the score matching and diffusion Monte
Carlo methods, we derive a weighted score matching objective to guide our
score-based models to converge correctly to ground states. We first evaluate
our approach with experiments on quantum harmonic traps, and results show that
it can accurately learn ground states of atomic systems. By implicitly modeling
high-dimensional data distributions, our work paves the way toward a more
efficient representation of quantum systems.

本研究提出了一个新的用于计算量子多体基态性质的优化框架，该方法通过基于 Langevin 动力学的梯度分数进行抽样，避免了显式概率分布，采用加权分数匹配目标引导模型正确收敛到基态，测例表明其能准确地学习原子系统的基态，并为量子系统的更高效表示铺平了道路。