Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2607.18865

Enhanced NQS via Annealed Gradient Descent

Shiwei Zhou, Yiming Huang, Xiao Yuan, Xiaoxia Cai

quant-phcs.LGphysics.chem-phphysics.comp-phSubmitted Jul 21, 2026• Announced Jul 22, 2026• 0 citations
v1 · Jul 21, 2026v2 · Jul 22, 2026
arXivHTMLPDF

Abstract

Neural quantum states offer expressive representations of quantum many-body wave functions, yet their practical accuracy can be limited by stochastic optimization rather than representational capacity. Here we identify a finite-sample instability, termed subspace trapping, in which physically important configurations become strongly underestimated, remain absent from successive sampling batches and receive insufficient gradient feedback. This self-reinforcing loss of sampled support can confine optimization to an effective subspace and produce apparently stationary states above the true ground state energy. To address this problem, we introduce annealed gradient descent (AGD), a sampling-aware update with annealing factor that temporarily increases the relative contribution of sampled low-probability configurations while limiting the dominance of high-probability ones. We establish the connection between finite-sample support loss and effective subspace optimization, and then evaluate the method across molecular systems, one and two-dimensional $J_1$-$J_2$ models. Annealed gradient descent suppresses metastable trapping, preserves physically relevant configurations and enables compact neural quantum states to attain chemical accuracy and competitive state-of-the-art performance. These results establish AGD as a lightweight complement to expressive neural architectures, improved sampling strategies for scalable quantum many-body optimization.

Related papers

Efficient optimization of neural network backflow for ab-initio quantum chemistry

An-Jun Liu, Bryan K. Clark

The ground state of second-quantized quantum chemistry Hamiltonians is key to determining molecular properties. Neural quantum states (NQS) offer flexible and expressive wavefunction ansatze for this task but face two main challenges: highly peaked ground-state wavefunctions hinder efficient sampling, and local energy evaluations scale quartically with system size, incurring significant computational costs. In this work, we overcome these challenges by introducing a suite of algorithmic enhancements, which includes efficient periodic compact subspace construction, truncated local energy evaluations, improved stochastic sampling, and physics-informed modifications. Applying these techniques to the neural network backflow (NNBF) ansatz, we demonstrate significant gains in both accuracy and scalability. Our enhanced method surpasses traditional quantum chemistry methods like CCSD and CCSD(T), outperforms other NQS approaches, and achieves competitive energies with state-of-the-art ab initio techniques such as HCI, ASCI, FCIQMC, and DMRG. A series of ablation and comparative studies quantifies the contribution of each enhancement to the observed improvements in accuracy and efficiency. Furthermore, we investigate the representational capacity of the ansatz, finding that its performance correlates with the inverse participation ratio (IPR), with more delocalized states being more challenging to approximate.

arXiv:2502.18843•Feb 26, 2025•0 citations

One More Time: Revisiting Neural Quantum States from a Reinforcement Learning Perspective

Juan Agustín Duque, Sergio García Heredia, Vinicius Hernandes +4 more

Neural quantum states (NQS) provide a flexible and scalable framework for approximating quantum many-body wavefunctions. Among NQS parameterizations, autoregressive models are especially attractive because they enable exact, independent sampling from the Born distribution, avoiding the autocorrelation and mixing issues of Markov chain methods. Yet their optimization remains comparatively underexplored: Adam is a scalable method but ignores function space geometry, while stochastic reconfiguration is principled but costly and numerically fragile in large models. To address this gap, we show that variational energy minimization can be viewed as an advantage policy-gradient problem over the Born distribution, motivating trust-region optimization for NQS training. We introduce Proximal Wavefunction Optimization (PWO), a principled trust-region algorithm that clips probability-ratio changes in the amplitude channel and phase increments in the phase channel. PWO avoids explicit matrix inversion, reuses samples across multiple updates, and combines the scalability of first-order optimization with theoretical guarantees. Across Ising and frustrated $J_1$-$J_2$ one- and two-dimensional spin systems, PWO improves stability and wall-clock convergence over Adam, minSR, and SPRING. Finally, we fine-tune a $1.5$B-parameter RWKV-7 model, demonstrating NQS optimization at a scale over three orders of magnitude beyond prior work.

cs.LGCross-listedarXiv:2607.02292•Jul 3, 2026•0 citations

Efficient optimization of neural network backflow for a b i n i t i o quantum chemistry

An-Jun Liu, Bryan K. Clark

The ground state of second-quantized quantum chemistry Hamiltonians is key to determining molecular properties. Neural quantum states (NQSs) offer flexible and expressive wave-function Ans\"atze for this task but face two main challenges: highly peaked ground-state wave functions hinder efficient sampling, and local energy evaluations scale quartically with system size, incurring significant computational costs. In this work, we overcome these challenges by introducing a suite of algorithmic enhancements, which includes efficient periodic compact subspace construction, truncated local energy evaluations, improved stochastic sampling, and physics-informed modifications. Applying these techniques to the neural network backflow Ansatz, we demonstrate significant gains in both accuracy and scalability. Our enhanced method surpasses traditional quantum chemistry methods like coupled cluster singles and doubles (CCSD) and CCSD and perturbative triples [CCSD(T)], outperforms other NQS approaches, and achieves competitive energies with state-of-the-art ab initio techniques such as heat-bath configuration interaction, adaptive sampling configuration interaction, full configuration interaction quantum Monte Carlo, and density matrix renormalization group. A series of ablation and comparative studies quantifies the contribution of each enhancement to the observed improvements in accuracy and efficiency. Furthermore, we investigate the representational capacity of the Ansatz, finding that its performance correlates with the inverse participation ratio, with more delocalized states being more challenging to approximate.

Physical review. B./Physical review. B•Sep 23, 2025•4 citations

Neural network quantum state with proximal optimization: a ground-state searching scheme based on variational Monte Carlo

Feng Chen, Ming Xue

Neural network quantum states (NQS), incorporating with variational Monte Carlo (VMC) method, are shown to be a promising way to investigate quantum many-body physics. Whereas vanilla VMC methods perform one gradient update per sample, we introduce a novel objective function with proximal optimization (PO) that enables multiple updates via reusing the mismatched samples. Our VMC-PO method keeps the advantage of the previous importance sampling gradient optimization algorithm [L. Yang, {\it et al}, Phys. Rev. Research {\bf 2}, 012039(R)(2020)] that efficiently uses sampled states. PO mitigates the numerical instabilities during network updates, which is similar to stochastic reconfiguration (SR) methods, but achieves an alternative and simpler implement with lower computational complexity. We investigate the performance of our VMC-PO algorithm for ground-state searching with a 1-dimensional transverse-field Ising model and 2-dimensional Heisenberg antiferromagnet on a square lattice, and demonstrate that the reached ground-state energies are comparable to state-of-the-art results.

arXiv:2210.16493•Oct 29, 2022•0 citations

Quantum Geometric Tensor Preconditioning for Stable Training of Recurrent Neural Quantum States

Adil Attar, Amine M. Aboussalah, Mohamed Hibat-Allah

Neural Quantum States (NQS) provide a powerful neural network-based variational framework for representing many-body wave functions and solving for ground states. Recurrent Neural Networks (RNNs) are particularly promising owing to their relatively low computational cost and their autoregressive property, which enables perfect sampling. Recently, RNNs have been reported to be unstable under curvature-based optimizers such as the minimum-step stochastic reconfiguration (minSR) method. In this paper, we address this perceived limitation and show that minSR can be stabilized through simple regularization techniques, enabling robust training of RNN-based NQS with only a few samples. Our approach outperforms the Adam optimizer on the one-dimensional transverse-field Ising model and the one-dimensional cluster state, and provides competitive results on the two-dimensional Heisenberg and $J_1-J_2$ models. This work offers a promising pathway for using modern optimization techniques with autoregressive NQS to address open questions in quantum simulation.

cond-mat.dis-nnCross-listedarXiv:2608.18065•Aug 19, 2026•0 citations

Quantum-Enhanced Neural Networks for Quantum Many-Body Simulations

Zongkang Zhang, Ying Li, Xiaosi Xu

Neural quantum states (NQS) have gained prominence in variational quantum Monte Carlo methods in approximating ground-state wavefunctions. Despite their success, they face limitations in optimization, scalability, and expressivity in addressing certain problems. In this work, we propose a quantum-neural hybrid framework that combines parametrized quantum circuits with neural networks to model quantum many-body wavefunctions. This approach combines the efficient sampling and optimization capabilities of autoregressive neural networks with the enhanced expressivity provided by quantum circuits. Numerical simulations demonstrate the scalability and accuracy of the hybrid ansatz in spin systems and quantum chemistry problems. Our results reveal that the hybrid method achieves notably lower relative energy compared to stand-alone NQS. These findings underscore the potential of quantum-neural hybrid methods for tackling challenging problems in quantum many-body simulations.

arXiv:2501.12130•PRX Intelligence•Jul 28, 2026•1 citation
Neural quantum states offer expressive representations of quantum many-body wave functions, yet their practical accuracy can be limited by stochastic optimization rather than representational capacity. Here we identify a finite-sample instability, termed subspace trapping, in which physically important configurations become strongly underestimated, remain absent from successive sampling batches and receive insufficient gradient feedback. This self-reinforcing loss of sampled support can confine optimization to an effective subspace and produce apparently stationary states above the true ground state energy. To address this problem, we introduce annealed gradient descent (AGD), a sampling-aware update with annealing factor that temporarily increases the relative contribution of sampled low-probability configurations while limiting the dominance of high-probability ones. We establish the connection between finite-sample support loss and effective subspace optimization, and then evaluate the method across molecular systems, one and two-dimensional J1J_1J1​-J2J_2J2​ models. Annealed gradient descent suppresses metastable trapping, preserves physically relevant configurations and enables compact neural quantum states to attain chemical accuracy and competitive state-of-the-art performance. These results establish AGD as a lightweight complement to expressive neural architectures, improved sampling strategies for scalable quantum many-body optimization.
The ground state of second-quantized quantum chemistry Hamiltonians is key to determining molecular properties. Neural quantum states (NQS) offer flexible and expressive wavefunction ansatze for this task but face two main challenges: highly peaked ground-state wavefunctions hinder efficient sampling, and local energy evaluations scale quartically with system size, incurring significant computational costs. In this work, we overcome these challenges by introducing a suite of algorithmic enhancements, which includes efficient periodic compact subspace construction, truncated local energy evaluations, improved stochastic sampling, and physics-informed modifications. Applying these techniques to the neural network backflow (NNBF) ansatz, we demonstrate significant gains in both accuracy and scalability. Our enhanced method surpasses traditional quantum chemistry methods like CCSD and CCSD(T), outperforms other NQS approaches, and achieves competitive energies with state-of-the-art ab initio techniques such as HCI, ASCI, FCIQMC, and DMRG. A series of ablation and comparative studies quantifies the contribution of each enhancement to the observed improvements in accuracy and efficiency. Furthermore, we investigate the representational capacity of the ansatz, finding that its performance correlates with the inverse participation ratio (IPR), with more delocalized states being more challenging to approximate.
Neural quantum states (NQS) provide a flexible and scalable framework for approximating quantum many-body wavefunctions. Among NQS parameterizations, autoregressive models are especially attractive because they enable exact, independent sampling from the Born distribution, avoiding the autocorrelation and mixing issues of Markov chain methods. Yet their optimization remains comparatively underexplored: Adam is a scalable method but ignores function space geometry, while stochastic reconfiguration is principled but costly and numerically fragile in large models. To address this gap, we show that variational energy minimization can be viewed as an advantage policy-gradient problem over the Born distribution, motivating trust-region optimization for NQS training. We introduce Proximal Wavefunction Optimization (PWO), a principled trust-region algorithm that clips probability-ratio changes in the amplitude channel and phase increments in the phase channel. PWO avoids explicit matrix inversion, reuses samples across multiple updates, and combines the scalability of first-order optimization with theoretical guarantees. Across Ising and frustrated J1J_1J1​-J2J_2J2​ one- and two-dimensional spin systems, PWO improves stability and wall-clock convergence over Adam, minSR, and SPRING. Finally, we fine-tune a 1.51.51.5B-parameter RWKV-7 model, demonstrating NQS optimization at a scale over three orders of magnitude beyond prior work.
The ground state of second-quantized quantum chemistry Hamiltonians is key to determining molecular properties. Neural quantum states (NQSs) offer flexible and expressive wave-function Ans\"atze for this task but face two main challenges: highly peaked ground-state wave functions hinder efficient sampling, and local energy evaluations scale quartically with system size, incurring significant computational costs. In this work, we overcome these challenges by introducing a suite of algorithmic enhancements, which includes efficient periodic compact subspace construction, truncated local energy evaluations, improved stochastic sampling, and physics-informed modifications. Applying these techniques to the neural network backflow Ansatz, we demonstrate significant gains in both accuracy and scalability. Our enhanced method surpasses traditional quantum chemistry methods like coupled cluster singles and doubles (CCSD) and CCSD and perturbative triples [CCSD(T)], outperforms other NQS approaches, and achieves competitive energies with state-of-the-art ab initio techniques such as heat-bath configuration interaction, adaptive sampling configuration interaction, full configuration interaction quantum Monte Carlo, and density matrix renormalization group. A series of ablation and comparative studies quantifies the contribution of each enhancement to the observed improvements in accuracy and efficiency. Furthermore, we investigate the representational capacity of the Ansatz, finding that its performance correlates with the inverse participation ratio, with more delocalized states being more challenging to approximate.
Neural network quantum states (NQS), incorporating with variational Monte Carlo (VMC) method, are shown to be a promising way to investigate quantum many-body physics. Whereas vanilla VMC methods perform one gradient update per sample, we introduce a novel objective function with proximal optimization (PO) that enables multiple updates via reusing the mismatched samples. Our VMC-PO method keeps the advantage of the previous importance sampling gradient optimization algorithm [L. Yang, {\it et al}, Phys. Rev. Research {\bf 2}, 012039(R)(2020)] that efficiently uses sampled states. PO mitigates the numerical instabilities during network updates, which is similar to stochastic reconfiguration (SR) methods, but achieves an alternative and simpler implement with lower computational complexity. We investigate the performance of our VMC-PO algorithm for ground-state searching with a 1-dimensional transverse-field Ising model and 2-dimensional Heisenberg antiferromagnet on a square lattice, and demonstrate that the reached ground-state energies are comparable to state-of-the-art results.
Neural Quantum States (NQS) provide a powerful neural network-based variational framework for representing many-body wave functions and solving for ground states. Recurrent Neural Networks (RNNs) are particularly promising owing to their relatively low computational cost and their autoregressive property, which enables perfect sampling. Recently, RNNs have been reported to be unstable under curvature-based optimizers such as the minimum-step stochastic reconfiguration (minSR) method. In this paper, we address this perceived limitation and show that minSR can be stabilized through simple regularization techniques, enabling robust training of RNN-based NQS with only a few samples. Our approach outperforms the Adam optimizer on the one-dimensional transverse-field Ising model and the one-dimensional cluster state, and provides competitive results on the two-dimensional Heisenberg and J1−J2J_1-J_2J1​−J2​ models. This work offers a promising pathway for using modern optimization techniques with autoregressive NQS to address open questions in quantum simulation.
Neural quantum states (NQS) have gained prominence in variational quantum Monte Carlo methods in approximating ground-state wavefunctions. Despite their success, they face limitations in optimization, scalability, and expressivity in addressing certain problems. In this work, we propose a quantum-neural hybrid framework that combines parametrized quantum circuits with neural networks to model quantum many-body wavefunctions. This approach combines the efficient sampling and optimization capabilities of autoregressive neural networks with the enhanced expressivity provided by quantum circuits. Numerical simulations demonstrate the scalability and accuracy of the hybrid ansatz in spin systems and quantum chemistry problems. Our results reveal that the hybrid method achieves notably lower relative energy compared to stand-alone NQS. These findings underscore the potential of quantum-neural hybrid methods for tackling challenging problems in quantum many-body simulations.