The electronic Schrödinger equation can only be solved analytically for the hydrogen atom, and the numerically exact full configuration-interaction method is exponentially expensive in the number of electrons. Quantum Monte Carlo methods are a possible way out: they scale well for large molecules, they can be parallelized and their accuracy has, as yet, been only limited by the flexibility of the wavefunction ansatz used. Here we propose PauliNet, a deep-learning wavefunction ansatz that achieves nearly exact solutions of the electronic Schrödinger equation for molecules with up to 30 electrons. PauliNet has a multireference Hartree–Fock solution built in as a baseline, incorporates the physics of valid wavefunctions and is trained using variational quantum Monte Carlo. PauliNet outperforms previous state-of-the-art variational ansatzes for atoms, diatomic molecules and a strongly correlated linear H₁₀, and matches the accuracy of highly specialized quantum chemistry methods on the transition-state energy of cyclobutadiene, while being computationally efficient.

电子薛定谔方程只能对氢原子进行解析求解，而数值精确的全构型相互作用方法在电子数量方面呈指数级昂贵。量子蒙特卡罗方法是一种可能的出路：它们可以很好地适用于大分子，它们可以并行化，并且它们的准确性迄今为止仅受到所使用的波函数 ansatz 的灵活性的限制。在这里，我们提出了 PauliNet，这是一种深度学习波函数 ansatz，它可以为具有多达 30 个电子的分子实现电子薛定谔方程的几乎精确解。PauliNet 有一个内置的多参考 Hartree-Fock 解决方案作为基线，结合了有效波函数的物理特性，并使用变分量子 Monte Carlo 进行训练。PauliNet 优于以前最先进的原子变分分析，₁₀，并且与高度专业化的量子化学方法对环丁二烯的过渡态能量的准确性相匹配，同时具有计算效率。