Princeton University Machine Learning in Physics

Excited states of quantum systems are relevant for photochemistry, quantum dots, semiconductors and more, but remain extremely challenging to calculate by conventional computational methods. In recent years tools from machine learning have found useful application in computational quantum mechanics, especially in making ground state calculations much more accurate. In this talk I will present a new algorithm for estimating the lowest excited states of a quantum system which works extremely well with deep neural networks. 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. 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 to atomic, nuclear, and condensed matter physics.