We present a variational Monte Carlo algorithm for estimating the lowest excited states of a quantum system which is a natural generalization of the estimation of ground states. The method has no free parameters and requires no explicit orthogonalization of the different states, instead transforming the problem of finding excited states of a given system into that of finding the ground state of an expanded system. Expected values of arbitrary observables can be calculated, including off-diagonal expectations between different states such as the transition dipole moment. Although the method is entirely general, it works particularly well in conjunction with recent work on using neural networks as variational Ansatze for many-electron systems, and we show that by combining this method with the FermiNet and Psiformer Ansatze we can accurately recover vertical excitation energies and oscillator strengths on molecules as large as benzene. Beyond the examples on molecules presented here, we expect this technique will be of great interest for applications of variational quantum Monte Carlo to atomic, nuclear and condensed matter physics.

翻译：我们提出了一种变分蒙特卡洛算法，用于估算量子系统的最低激发态，该算法是基态估算的自然推广。该方法无自由参数，且无需对不同态进行显式正交化，而是将给定系统的激发态求解问题转换为扩展系统的基态求解问题。可计算任意可观测量（包括不同态之间的非对角期望值，如跃迁偶极矩）的期望值。尽管该方法具有完全通用性，但结合近期将神经网络作为多电子系统变分拟设的研究，其效果尤为显著。我们展示了通过将该方法与费米网和Psiformer拟设相结合，可精确获取苯等大分子的垂直激发能与振子强度。除本文列举的分子实例外，我们预期该技术将对变分量子蒙特卡洛在原子物理、核物理及凝聚态物理中的应用产生重要价值。