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IEEE Transactions on Parallel and Distributed Systems

Fast and Scalable Neural Network Quantum States Method for Molecular Potential Energy Surfaces

Yangjun Wu, Wanlu Cao, Jiacheng Zhao, Honghui Shang

Published May 12, 2025• 4 citations
Publisher

Abstract

The Neural Network Quantum States (NNQS) method is highly promising for accurately solving the Schrödinger equation, yet it encounters challenges such as computational demands and slow rates of convergence. To address the high computational requirements, we introduce optimizations including a cross-sample KV cache sharing technique to enhance sampling efficiency, Quantum Bitwise and BloomHash methods for more efficient local energy computation, and mixed-precision training strategies to boost computational efficiency. To overcome the issue of slow convergence, we propose a parallel training algorithm for NNQS under second quantization to accelerate the training of base models for molecular potential surfaces. Our approach achieves up to 27-fold acceleration specifically in local energy calculations in systems with 154 spin orbitals and demonstrates strong and weak scaling efficiencies of 98% and 97%, respectively, on the H$_{2}$O$_{2}$potential surface training set. The parallelized implementation of transformer-based NNQS is highly portable on various high-performance computing architectures, offering new perspectives on quantum chemistry simulations.

DOI
10.1109/tpds.2025.3568360

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•Nov 26, 2025•0 citations
The Neural Network Quantum States (NNQS) method is highly promising for accurately solving the Schrödinger equation, yet it encounters challenges such as computational demands and slow rates of convergence. To address the high computational requirements, we introduce optimizations including a cross-sample KV cache sharing technique to enhance sampling efficiency, Quantum Bitwise and BloomHash methods for more efficient local energy computation, and mixed-precision training strategies to boost computational efficiency. To overcome the issue of slow convergence, we propose a parallel training algorithm for NNQS under second quantization to accelerate the training of base models for molecular potential surfaces. Our approach achieves up to 27-fold acceleration specifically in local energy calculations in systems with 154 spin orbitals and demonstrates strong and weak scaling efficiencies of 98% and 97%, respectively, on the H2_{2}2​O2_{2}2​potential surface training set. The parallelized implementation of transformer-based NNQS is highly portable on various high-performance computing architectures, offering new perspectives on quantum chemistry simulations.
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.
Solving quantum many-body problems is one of the fundamental challenges in quantum chemistry. While neural network quantum states (NQS) have emerged as a promising computational tool, its training process incurs exponentially growing computational demands, becoming prohibitively expensive for large-scale molecular systems and creating fundamental scalability barriers for real-world applications. To address the above challenges, we present QChem-Trainer, a highperformance NQS training framework for ab initio electronic structure calculations. First, we propose a scalable sampling parallelism strategy with multi-layer workload division and hybrid sampling scheme, which breaks the scalability barriers in large-scale NQS training. Second, we introduce multi-level energy calculation parallelism, enabling more efficient local energy computation in NQS training. Last, we employ cachecentric optimization for transformer-based ansatz and incorporate it with sampling parallelism strategy, which further accelerates the NQS training and achieves stable memory footprints at scale. Experiments demonstrate that QChem-Trainer provides up to8.41×8.41 \times8.41×speedup in NQS training and attains a parallel efficiency of up to 95.8% when scaling to 1,536 nodes.
Neural Network Quantum States (NNQS) offer a powerful variational Monte Carlo (VMC) approach for quantum many-body problems, balancing polynomial scaling with high expressive power. However, scaling NNQS to large chemical systems faces challenges in preserving accuracy with exact energy and managing vast configurations efficiently. In this work, we introduce NNQS-SCI, a high-performance Selected Configuration Interaction (SCI) based NNQS method designed to overcome these limitations. NNQS-SCI employs highly parallelized Slater-Condon rules for fast local energy evaluations, avoiding accuracy loss, while its adaptive SCI engine dynamically manages billions of configurations without space explosion or arbitrary cutoffs that plague other NNQS-CI approaches. Optimized for extreme scalability via multi-level parallelism and memory compression, NNQS-SCI successfully simulates systems up to 152 spin orbitals, tackling Hilbert space dimensions exceeding 1014 and demonstrating significant advances in scale and efficiency. NNQS-SCI thus provides a robust and scalable path towards high-accuracy quantum chemistry on high-performance computing platforms.
Abstract Variational optimization of neural-network representations of quantum states has been successfully applied to solve interacting fermionic problems. Despite rapid developments, significant scalability challenges arise when considering molecules of large scale, which correspond to non-locally interacting quantum spin Hamiltonians consisting of sums of thousands or even millions of Pauli operators. In this work, we introduce scalable parallelization strategies to improve neural-network-based variational quantum Monte Carlo calculations for ab-initio quantum chemistry applications. We establish GPU-supported local energy parallelism to compute the optimization objective for Hamiltonians of potentially complex molecules. Using autoregressive sampling techniques, we demonstrate systematic improvement in wall-clock timings required to achieve coupled cluster with up to double excitations baseline target energies. The performance is further enhanced by accommodating the structure of resultant spin Hamiltonians into the autoregressive sampling ordering. The algorithm achieves promising performance in comparison with the classical approximate methods and exhibits both running time and scalability advantages over existing neural-network based methods.
The field of quantum chemistry has long been defined by the central computational challenge of the quantum many-body fermionic system problem, main the electronic Schrödinger equation. This exponential scaling makes it computationally intractable to solve, the exact governing electronic Schrödinger equation. Approximation methods have been developed, ranging from the widely used Density Functional Theory (DFT) to Coupled Cluster (CC) theory. While powerful, these conventional approaches often involve controlled truncations which caused a trade-off between accuracy, leaving many systems—particularly those with strong electron correlation—beyond the reach of ab initio simulation. Furthermore, the famous fermionic sign oscillation problem is particularly severe in stochastic methods like Quantum Monte Carlo (QMC). 1 Traditional Ansätze are also frequently engineered specifically for particular systems, which results in a fragmentation of results and fundamentally limits the transferability. Recent research demonstrates that with carefully designed architectures, ANNs can not only represent ground states of model systems with high precision but also tackle the sign problem, offering a promising path forward for strongly correlated electronic structure calculations.2,3 This review charts the paradigm shift driven by Neural Network Quantum States (NNQS), which leverage the representational power of deep learning to overcome these barriers. We detail the architectural evolution from Restricted Boltzmann Machines to autoregressive models like RNNs and Transformers, which enable exact, uncorrelated sampling and bypass critical bottlenecks.2,4,5Furthermore, we explore the geometric foundation of high-efficiency optimization via the neural networks, which decouples optimization cost from model complexity.6 The frontier of the field is marked by the integration of operator learning and hybrid quantum-classical frameworks, such as Reinforcement Learning for contracted quantum eigen-solvers and Quantum-Enhanced Neural Networks, which leverage quantum processors to enhance expressivity for hardware-efficient Ansätze.7,8 By framing the problem through the lens of computational resource allocation—specifically, trading exponential memory demands for polynomialcomplexity optimization and sampling—this review elucidates how recent advances at the intersection of artificial neural networks and quantum computing have evolved. The emergence of those methods not merely progress into a powerful simulation-tools, but also a hybrid computational interface.9 This convergence offers a versatile and systematically improvable framework for potentially addressing some of the most challenging problems in quantum physics and chemistry.