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Journal of Chemical Theory and Computation

Transformer-Based Neural-Network Quantum State Method for Electronic Band Structures of Real Solids

Lizhong Fu, Yangjun Wu, Honghui Shang, Jinlong Yang

Published Jul 8, 2024• 18 citations
Publisher

Abstract

Recent advancements in neural networks have led to significant progress in addressing many-body electron correlations in small molecules and various physical models. In this work, we propose QiankunNet-Solid, which incorporates periodic boundary conditions into the neural network quantum state (NNQS) framework based on generative Transformer architecture along with a batched autoregressive sampling (BAS) method, enabling the effective ab initio calculation of real solid materials. The accuracy of this method is demonstrated in one-, two-, and three-dimensional periodic systems, with results comparable to those of full configuration interaction and coupled-cluster method, even in the strongly correlated regime. Furthermore, we compute the band structures and density of states for silicon crystal. The successful incorporation of periodic boundary conditions into the NNQS framework through QiankunNet-Solid opens up new possibilities for the accurate and efficient study of electronic structure properties in solid-state physics.

DOI
10.1021/acs.jctc.4c00567

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Neural network quantum state (NNQS) has emerged as a promising candidate for quantum many-body problems, but its practical applications are often hindered by the high cost of sampling and local energy calculation. We develop a high-performance NNQS method for \textit{ab initio} electronic structure calculations. The major innovations include: (1) A transformer based architecture as the quantum wave function ansatz; (2) A data-centric parallelization scheme for the variational Monte Carlo (VMC) algorithm which preserves data locality and well adapts for different computing architectures; (3) A parallel batch sampling strategy which reduces the sampling cost and achieves good load balance; (4) A parallel local energy evaluation scheme which is both memory and computationally efficient; (5) Study of real chemical systems demonstrates both the superior accuracy of our method compared to state-of-the-art and the strong and weak scalability for large molecular systems with up to 120120120 spin orbitals.
Neural network quantum state (NNQS) has emerged as a promising candidate for quantum many-body problems, but its practical applications are often hindered by the high cost of sampling and local energy calculation. We develop a high-performance NNQS method for ab initio electronic structure calculations. The major innovations include: (1) A transformer based architecture as the quantum wave function ansatz; (2) A data-centric parallelization scheme for the variational Monte Carlo (VMC) algorithm which preserves data locality and well adapts for different computing architectures; (3) A parallel batch sampling strategy which reduces the sampling cost and achieves good load balance; (4) A parallel local energy evaluation scheme which is both memory and computationally efficient; (5) Study of real chemical systems demonstrates both the superior accuracy of our method compared to state-of-the-art and the strong and weak scalability for large molecular systems with up to 120 spin orbitals.
Establishing a predictive ab initio method for solid systems is one of the fundamental goals in condensed matter physics and computational materials science. We demonstrate that artificial neural networks can simulate first-principles calculations of extended periodic materials. The stochastic optimization of a highly expressive ansatz accurately provides the ground-state energy of a one-dimensional system up to the thermodynamic limit, reaching its chemical accuracy. The correlation energy is simulated precisely also for real solids in both two and three dimensions. We further show that multiple excited states corresponding to the quasiparticle band structure can be obtained with an additional small computation exploiting a technique developed from quantum simulations.
The neural network quantum state (NNQS) method has demonstrated promising results in ab initio quantum chemistry, achieving remarkable accuracy in molecular systems. However, efficient calculation of systems with large active spaces remains challenging. This study introduces a novel approach that bridges tensor network states with the transformer-based NNQS-Transformer (QiankunNet) to enhance accuracy and convergence for systems with relatively large active spaces. By transforming tensor network states into active space configuration interaction type wave functions, QiankunNet achieves accuracy surpassing both the pretraining density matrix renormalization group (DMRG) results and traditional coupled cluster methods, particularly in strongly correlated regimes. We investigate two configuration transformation methods: the sweep-based direct conversion (Conv.) method and the entanglement-driven genetic algorithm (EDGA) method, with Conv. showing superior efficiency. The effectiveness of this approach is validated on H 2 O with a large active space (10e, 24o) in the cc-pVDZ basis set, demonstrating an efficient routine between DMRG and QiankunNet and also offering a promising direction for advancing quantum state representation in complex molecular systems.
In recent years, neural network quantum states (NNQS) have emerged as powerful tools for the study of quantum many-body systems. Electronic structure calculations are one such canonical many-body problem that have attracted significant research efforts spanning multiple decades, whilst only recently being attempted with NNQS. However, the complex non-local interactions and high sample complexity are significant challenges that call for bespoke solutions. Here, we parameterise the electronic wavefunction with a novel autoregressive neural network (ARN) that permits highly efficient and scalable sampling, whilst also embedding physical priors reflecting the structure of molecular systems without sacrificing expressibility. This allows us to perform electronic structure calculations on molecules with up to 30 spin-orbitals -- at least an order of magnitude more Slater determinants than previous applications of conventional NNQS -- and we find that our ansatz can outperform the de-facto gold-standard coupled cluster methods even in the presence of strong quantum correlations. With a highly expressive neural network for which sampling is no longer a computational bottleneck, we conclude that the barriers to further scaling are not associated with the wavefunction ansatz itself, but rather are inherent to any variational Monte Carlo approach.