OSCR

Solving the Hubbard model with neural quantum states.

Overview

Authors: Yuntian Gu1,2, Wenrui Li1,2, Heng Lin2,3, Bo Zhan2,4, Ruichen Li1,2, Yifei Huang2, Di He1, Yantao Wu4, Tao Xiang4, Mingpu Qin5, Liwei Wang1, Dingshun Lv2,6
ORCID iDs: Yuntian Gu, Ruichen Li, Yifei Huang, Di He, Tao Xiang, Liwei Wang
  1. State Key Laboratory of General Artificial Intelligence, School of Intelligence Science and Technology, Peking University,Beijing, China
  2. ByteDance Seed, Beijing, China
  3. State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, Tsinghua University,Beijing, China
  4. Institute of Physics, Chinese Academy of Sciences,Beijing, China
  5. Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), School of Physics and Astronomy, Shanghai Jiao Tong University,Shanghai, China
  6. FieldQuantum Research Institute, Beijing, China
Institutions: Peking University (China); State Key Laboratory of Low-Dimensional Quantum Physics; Chinese Academy of Sciences (China); ByteDance (China) (China); Shanghai Jiao Tong University (China)
Journal: Nature communications, volume 17, issue 1, article 7838
Dates: received 9 October 2025; accepted 26 May 2026; published online 22 June 2026
Type: Research article · Language: English
License: CC BY-NC-ND
Identifiers: DOI 10.1038/s41467-026-74028-6 · PMID 42331803 · PMCID PMC13439271 · OpenAlex W7165563151
Open access: gold, a free copy (OpenAlex)
Status: code found, not verified yet
Methods: Statistics, Spectral & time-frequency, Machine learning
Keywords: Computational science, Electronic properties and materials, Quantum physics
Topic: Quantum many-body systems (Atomic and Molecular Physics, and Optics, Physics and Astronomy), according to OpenAlex
Funding: National Natural Science Foundation of China (2021ZD0301902, 62276005, 12488201, 12274290); Chinese Academy of Sciences; National Science and Technology Major Project (2022ZD0114902); National Key Research and Development Program of China (2021ZD0301902, 2022YFA1405400)
Citations: not cited yet (Europe PMC); 58 references in the paper

Abstract

The abstract is not reproduced here: the paper's license (CC BY-NC-ND) does not allow it. Read it in the paper, at the publisher or on Europe PMC.

Code

No file of the authors' code could be read here: it is described below, and read at its source.

codeocean:9301616

License: none: the authors keep all their rights
State: cannot be verified, verified on 27 September 2026
Evidence: found in the paper
Software Heritage: not checked
Found in: “Code availability”
Not found: README, license file, CITATION.cff, environment file, tests, continuous integration, documentation
Availability: 1 check, the latest on 27 September 2026: cannot be verified
  • 27 September 2026: cannot be verified
At the source: codeocean.com/capsule/9301616/tree

Code availability statement

The paper has a code availability statement. Its license (CC BY-NC-ND) does not allow reproducing it here; in short, from what the harvester recognized in it:

Read it in the paper: doi.org/10.1038/s41467-026-74028-6.

Tracing map

Proposed by the machine: these links were found in the paper and verified at the source, without human review. The map will receive a Zenodo DOI once one of the paper's authors has validated it with their ORCID.

What the map holds:

  • 1 repository of the authors' code, each at its verified commit, with its license and how the link was found in the paper;
  • 0 scripts, each with its path and the digest of its content;
  • no match between paragraphs and code yet;
  • neither the text of the paper nor the code itself.

Its JSON (tracing-map.json) is deposited on Zenodo with its DOI once the map is validated.

Data

No dataset and no data link were found in the paper.

Code and data availability statement

The paper has a code and data availability statement. Its license (CC BY-NC-ND) does not allow reproducing it here; in short, from what the harvester recognized in it:

Read it in the paper: doi.org/10.1038/s41467-026-74028-6.

Versions

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Version 2, 28 September 2026

  • Funding: added National Natural Science Foundation of China: 2021ZD0301902, 62276005, 12488201, 12274290; Chinese Academy of Sciences; National Science and Technology Major Project: 2022ZD0114902; National Key Research and Development Program of China: 2021ZD0301902, 2022YFA1405400

Version 1, 27 September 2026: the first record

Recorded: type, language, journal, volume, issue, pages, dates, 12 authors, 3 keywords, 44 references.

Cite

This paper

Gu, Y., Li, W., Lin, H., Zhan, B., Li, R., Huang, Y., He, D., Wu, Y., Xiang, T., Qin, M., Wang, L., & Lv, D. (2026). Solving the Hubbard model with neural quantum states. Nature communications, 17(1), 7838. https://doi.org/10.1038/s41467-026-74028-6

BibTeX

@article{gu2026solving,
author = {Gu, Yuntian and Li, Wenrui and Lin, Heng and Zhan, Bo and Li, Ruichen and Huang, Yifei and He, Di and Wu, Yantao and Xiang, Tao and Qin, Mingpu and Wang, Liwei and Lv, Dingshun},
title = {{Solving the Hubbard model with neural quantum states}},
journal = {Nature communications},
year = {2026},
month = jun,
volume = {17},
number = {1},
pages = {7838},
publisher = {Nature Publishing Group},
issn = {2041-1723},
doi = {10.1038/s41467-026-74028-6},
url = {https://doi.org/10.1038/s41467-026-74028-6},
pmid = {42331803},
pmcid = {PMC13439271}
}

RIS

TY - JOUR
AU - Gu, Yuntian
AU - Li, Wenrui
AU - Lin, Heng
AU - Zhan, Bo
AU - Li, Ruichen
AU - Huang, Yifei
AU - He, Di
AU - Wu, Yantao
AU - Xiang, Tao
AU - Qin, Mingpu
AU - Wang, Liwei
AU - Lv, Dingshun
TI - Solving the Hubbard model with neural quantum states
T2 - Nature communications
J2 - Nat Commun
PY - 2026
DA - 2026/06/22
VL - 17
IS - 1
SP - 7838
SN - 2041-1723
PB - Nature Publishing Group
DO - 10.1038/s41467-026-74028-6
UR - https://doi.org/10.1038/s41467-026-74028-6
LA - en
ER -

CSL-JSON

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