I will review variational quantum Monte Carlo as applied to arbitrary Hilbert spaces and Hamiltonians, and how wave-function ansatzes based on neural networks can be easily incorporated both in the first- and second-quantization formalisms. I will then demonstrate two applications to Hamiltonians relevant for quantum chemistry: First, an ab-initio electronic Hamiltonian for molecules in first quantization is solved with an antisymmetric ansatz that combines a physical baseline with a Jastrow factor and backflow parametrized by neural networks. Ground and excited states can be obtained with accuracy rivaling established quantum-chemistry methods. Second, a model exciton–phonon Hamiltonian in mixed first and second quantization is solved with an off-the-shelf convolutional neural network, improving upon state-of-the-art methods.
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