Hybrid tensor network and neural network quantum states for quantum chemistry

TL;DR

This paper introduces hybrid tensor network and neural network quantum states with novel ansatzes and algorithms, achieving chemical accuracy in complex molecular systems and advancing quantum chemistry simulations.

Contribution

The work presents new hybrid ansatzes combining tensor networks and neural networks, along with a semi-stochastic energy evaluation algorithm, improving accuracy and efficiency in quantum chemistry applications.

Findings

Achieved chemical accuracy in hydrogen chain H50

Successfully modeled iron-sulfur cluster [Fe2S2(SCH3)4]^{2-}

Demonstrated effectiveness on 3D hydrogen cluster H18

Abstract

Neural network quantum states (NQS) have emerged as a powerful and flexible framework for addressing quantum many-body problems. While successful for model Hamiltonians, their application to molecular systems remains challenging for several reasons. In this work, we introduce three innovations to overcome some of the key limitations. (1) We propose two novel ans\"atzet hat hybridize tensor network and neural network states for addressing initialization challenges and enhancing the expressivity of tensor networks. First, we develop a bounded-degree graph recurrent neural network (BDG-RNN) ansatz that leverages graph-based updates, enabling applications to molecular electronic structure problems. Second, we introduce restricted Boltzmann machine (RBM) inspired correlators to further enhance expressivity and improve accuracy, without dramatically modifying the underlying variational Monte Carlo (VMC) optimization framework. (2) We introduce a semi-stochastic algorithm for local energy evaluation, which significantly reduces computational cost while maintaining high accuracy. Combining these advances, we demonstrate that our approaches can achieve chemical accuracy in challenging systems, including the one-dimensional hydrogen chain H50, the iron-sulfur cluster [Fe2S2(SCH3)4]^{2-}, and a three-dimensional $3 \times 3 \times 2$ hydrogen cluster H18. These methods are implemented in an open-source package - PyNQS (https://github.com/Quantum-Chemistry-Group-BNU/PyNQS) to advance NQS methodologies for quantum chemistry.