Quantum-Inspired Tempering for Ground State Approximation using Artificial Neural Networks

Parameterized artificial neural networks (ANNs) have been shown to efficiently approximate to high accuracy ground states of numerous interesting quantum many-body Hamiltonians. However, the standard variational algorithms used to update the ANN parameters can get trapped in local minima even if the ANN is sufficiently expressive. To escape these local minima, we propose a method inspired by quantum parallel tempering, where we train multiple ANNs governed by Hamiltonians with different "driver" strengths and allow for the exchange of neighboring ANN parameterizations after a fixed number of training steps. We study instances from two classes of Hamiltonians. The first is based on a permutation-invariant Hamiltonian whose landscape stymies the standard training algorithm by drawing it to a false minimum. The second is the second quantized electronic structure Hamiltonian of four Hydrogen atoms arranged in a rectangle, which is then discretized using Gaussian basis functions. We study this problem in a minimal basis set, which exhibits false minima that can trap the standard variational algorithm despite the problem's small size. We show that our quantum parallel tempering inspired method is useful for finding good approximations to the ground states of these problems.