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.

我们提出了一种变分蒙特卡罗算法，可以估计量子系统的最低激发态，该方法是寻找扩展系统的基态，可以计算任意观测值的期望值，特别适用于利用神经网络作为变分试探态的许多电子系统。我们通过将该方法与FermiNet和Psiformer等试探态相结合，在苯等大分子上准确恢复了垂直激发能和振子强度，此技术对于变分量子蒙特卡罗在原子、核能和凝聚态物理等领域的应用具有重要意义。

自然量子蒙特卡洛计算激发态