Accurate computation of quantum excited states with neural networks
Abstract
We present an algorithm to estimate the excited states of a quantum system by variational Monte Carlo, which has no free parameters and requires no orthogonalization of the states, instead transforming the problem into that of finding the ground state of an expanded system. Arbitrary observables can be calculated, including off-diagonal expectations, such as the transition dipole moment. The method works particularly well with neural network ansätze, and by combining this method with the FermiNet and Psiformer ansätze, we can accurately recover excitation energies and oscillator strengths on a range of molecules. We achieve accurate vertical excitation energies on benzene-scale molecules, including challenging double excitations. Beyond the examples presented in this work, we expect that this technique will be of interest for atomic, nuclear, and condensed matter physics. Editor’s summary Excited states are important in many areas of physics and chemistry; however, scalable, accurate, and robust calculations of excited-state properties from first principles remain a critical theoretical challenge. Recent advances in computing the ground-state properties of molecular systems driven by deep learning demonstrate that this technique has the potential to address this problem. Pfau et al. present a parameter-free mathematical principle for computing excited states using deep neural networks by directly generalizing variational quantum Monte Carlo to ground states. The proposed…
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