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This study introduces Projected Inverse Iteration (PII), an algorithm that reframes ground-state search as an eigenvalue problem to overcome the spectral gap limitations of standard optimization methods in neural quantum states. By achieving rapid, gap-insensitive convergence while maintaining polynomial scaling, PII offers a robust solution for simulating complex quantum systems like frustrated magnets. Beyond quantum computing, the technique's interpretation as a specialized natural gradient method suggests potential applications for solving related eigenvalue challenges in broader deep learning contexts.
Projected Inverse Iteration: An Eigenvalue Approach to Ground-State Computation with Neural Quantum States
arXiv:2606.07825v1 Announce Type: new Abstract: Deep learning offers a powerful approach to quantum many-body problems via neural network wavefunctions, but their optimization remains a severe bottleneck. Existing optimization methods, including natural gradient descent and stochastic reconfiguration, suffer from spectral gap-dependent convergence that limits their effectiveness on systems fraught with competing orders and nearly degenerate ground states, such as frustrated magnets and strongly correlated electron materials. Here, we introduce Projected Inverse Iteration (PII) by re-framing the ground-state search as an eigenvalue problem. PII achieves rapid, gap-insensitive convergence while preserving the favorable polynomial computational scaling of stochastic reconfiguration. Demonstrated on challenging two-dimensional spin systems, including the highly frustrated $J_1$-$J_2$ model, PII outperforms standard optimization techniques and presents a promising algorithmic strategy for discovering complex quantum states in the presence of small spectral gaps. More broadly, PII can be interpreted as a novel natural gradient method tailored for eigenvalue problems, opening up its application to related challenges within deep learning.
Abstract:Deep learning offers a powerful approach to quantum many-body problems via neural network wavefunctions, but their optimization remains a severe bottleneck. Existing optimization methods, including natural gradient descent and stochastic reconfiguration, suffer from spectral gap-dependent convergence that limits their effectiveness on systems fraught with competing orders and nearly degenerate ground states, such as frustrated magnets and strongly correlated electron materials. Here, we introduce Projected Inverse Iteration (PII) by re-framing the ground-state search as an eigenvalue problem. PII achieves rapid, gap-insensitive convergence while preserving the favorable polynomial computational scaling of stochastic reconfiguration. Demonstrated on challenging two-dimensional spin systems, including the highly frustrated $J_1$-$J_2$ model, PII outperforms standard optimization techniques and presents a promising algorithmic strategy for discovering complex quantum states in the presence of small spectral gaps. More broadly, PII can be interpreted as a novel natural gradient method tailored for eigenvalue problems, opening up its application to related challenges within deep learning.
arXiv:2606.07825 [quant-ph]
(or arXiv:2606.07825v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2606.07825 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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