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

• URL: http://arxiv.org/abs/2210.11405v2
• Date: Wed, 16 Nov 2022 17:23:33 GMT
• Title: Quantum-Inspired Tempering for Ground State Approximation using Artificial Neural Networks
• Authors: Tameem Albash, Conor Smith, Quinn Campbell, Andrew D. Baczewski
• Abstract summary: We propose a parallel tempering method that facilitates escape from local minima. We show that augmenting the training with quantum parallel tempering becomes useful to finding good approximations to the ground states of problem instances.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: A large body of work has demonstrated that parameterized artificial neural networks (ANNs) can efficiently describe ground states of numerous interesting quantum many-body Hamiltonians. However, the standard variational algorithms used to update or train the ANN parameters can get trapped in local minima, especially for frustrated systems and even if the representation is sufficiently expressive. We propose a parallel tempering method that facilitates escape from such local minima. This methods involves training multiple ANNs independently, with each simulation governed by a Hamiltonian with a different "driver" strength, in analogy to quantum parallel tempering, and it incorporates an update step into the training that allows for the exchange of neighboring ANN configurations. We study instances from two classes of Hamiltonians to demonstrate the utility of our approach. The first instance is based on a permutation-invariant Hamiltonian whose landscape stymies the standard training algorithm by drawing it increasingly to a false local minimum. The second instance is four hydrogen atoms arranged in a rectangle, which is an instance of the second quantized electronic structure Hamiltonian 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 augmenting the training with quantum parallel tempering becomes useful to finding good approximations to the ground states of these problem instances.

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