Artificial neural networks for quantum state representation

Illustration of an artificial neural network.
Illustration of a quantum circuit.
Illustration of a qubit state.

We use generative artificial neural networks, such as restricted Boltzmann machines and recurrent neural networks, as a variationa ansatz to reconstruct quantum many-body systems.

We consider two ways to train the networks. One way is to use data generated via projective measurements from an experimentally prepared or numerically simulated quantum state. We train the generative neural network to encode the probability distribution underlying the data and once trained we use it to generate additional measurement data.

The second approach is based on variational Monte Carlo. We train the generative neural network to minimize the energy expectation value of a given Hamiltonian and represent the ground state. We then generate measurement data from this reconstructed state.

We have shown that the combination of two approaches is a promising method to advance the performance of variational Monte Carlo with a limited amount of measurement data.

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