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We address this bottleneck by introducing the implicitly restarted Lanczos (IRL) method as the core engine for NQS training. Our approach recasts the parameter update problem into a Hermitian eigenvalue problem that IRL solves efficiently, automatically determining the optimal descent direction and step size without hyperparameter tuning. We demonstrate that IRL enables shallow NQS architectures to achieve extreme precision in just 3\u20135 optimization steps, dramatically outperforming existing methods, including minimum-step stochastic reconfiguration (MinSR). For the N2 dissociation curve, IRL successfully trains a shallow NQS to match full configuration interaction accuracy, validating its robust convergence in strongly correlated regimes. This work establishes IRL as an efficient and robust second-order optimization strategy for variational quantum models.<\/jats:p>","DOI":"10.1021\/prechem.5c00445","type":"journal-article","created":{"date-parts":[[2026,3,30]],"date-time":"2026-03-30T12:55:14Z","timestamp":1774875314000},"page":"1395-1404","source":"Crossref","is-referenced-by-count":1,"title":["Implicitly Restarted\nLanczos Enables Chemically Accurate\nShallow Neural Quantum States"],"prefix":"10.1021","volume":"4","author":[{"ORCID":"https:\/\/orcid.org\/0009-0006-7686-929X","authenticated-orcid":true,"given":"Wei","family":"Liu","sequence":"first","affiliation":[{"name":"Westlake University , , , ,","place":["Hangzhou, Zhejiang, China, 310030"]},{"name":"Westlake Institute for Advanced Study , , , ,","place":["Hangzhou, Zhejiang, China, 310024"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5410-6183","authenticated-orcid":true,"given":"Wenjie","family":"Dou","sequence":"additional","affiliation":[{"name":"Westlake University , , , ,","place":["Hangzhou, Zhejiang, China, 310030"]},{"name":"Westlake Institute for Advanced Study , , , ,","place":["Hangzhou, Zhejiang, China, 310024"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"316","published-online":{"date-parts":[[2026,3,30]]},"reference":[{"key":"2026092808080778000_cit1","doi-asserted-by":"publisher","first-page":"602","DOI":"10.1126\/science.aag2302","article-title":"Solving the quantum many-body problem with artificial\nneural networks","volume":"355","author":"Carleo","year":"2017","journal-title":"Science"},{"key":"2026092808080778000_cit2","doi-asserted-by":"publisher","first-page":"040501","DOI":"10.1088\/2058-9565\/ad7168","article-title":"From architectures\nto applications: A review of neural quantum states","volume":"9","author":"Lange","year":"2024","journal-title":"Quantum Sci. 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