Variational benchmarks for quantum many-body problems
Open accessAbstract
The continued development of computational approaches to many-body ground-state problems in physics and chemistry calls for a consistent way to assess its overall progress. In this work, we introduce a metric of variational accuracy, the V-score, obtained from the variational energy and its variance. We provide an extensive curated dataset of variational calculations of many-body quantum systems, identifying cases where state-of-the-art numerical approaches show limited accuracy and future algorithms or computational platforms, such as quantum computing, could provide improved accuracy. The V-score can be used as a metric to assess the progress of quantum variational methods toward a quantum advantage for ground-state problems, especially in regimes where classical verifiability is impossible.
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For the ground-state problem, variational Monte Carlo method provides a numerical method for ground-state estimation that is competitive with other state-of-the-art approaches such as tensor networks or quantum Monte Carlo.
“For the ground-state problem, the variational Monte Carlo method 130 provides a numerical method for ground-state estimation that is competitive with other state-of-the-art approaches such as tensor networks or quantum Monte Carlo 131 .”
From Beyond-classical computation in quantum simulation (2025) · cites this paper as [131]
The Variational Monte Carlo section (p. 13) describes VMC as a tractable method for finding ground states, and the comparison section (p. 21) reports that VMC-based neural quantum states outperform traditional methods on certain 2D models. But the paper makes that comparison for specific systems; it does not establish that VMC is generally competitive with tensor networks or quantum Monte Carlo. The Quantum Monte Carlo section (p. 19) instead describes QMC results as accuracy benchmarks for variational methods. (LLM, conf=0.84)
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References 146 · Cited by 79
Research works printed but not linked: 23
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- Authors
- Wu, D., Rossi, R., Vicentini, F., Astrakhantsev, N., Becca, F., Cao, X., Carrasquilla, J., Ferrari, F., Georges, A., Hibat-Allah, M., Imada, M., Läuchli, A. M., Mazzola, G., Mezzacapo, A., Millis, A., Robledo Moreno, J., Neupert, T., Nomura, Y., Nys, J., Parcollet, O., Pohle, R., Romero, I., Schmid, M., Silvester, J. M., Sorella, S., Tocchio, L. F., Wang, L., White, S. R., Wietek, A., Yang, Q., Yang, Y., Zhang, S., & Carleo, G.
- Affiliations
- École Polytechnique Fédérale de Lausanne (CH)
- Centre National de la Recherche Scientifique (FR)
- University of Zurich (CH)
- University of Trieste (IT)
- Flatiron Institute (US)
- ETH Zurich (CH)
- Goethe University Frankfurt (DE)
- University of Geneva (CH)
- University of Waterloo (CA)
- Waseda University (JP)
- Paul Scherrer Institute (CH)
- IBM (United States) (US)
- Center for Computational Quantum Physics, Flatiron Institute, New York, NY 10010, USA.
- Tohoku University (JP)
- University of California, Irvine (US)
- Scuola Internazionale Superiore di Studi Avanzati (IT)
- Politecnico di Torino (IT)
- Chinese Academy of Sciences (CN)
- Max Planck Institute for the Physics of Complex Systems (DE)
- William & Mary (US)
- Corresponding author
- Carleo, Giuseppe
- ORCID
- Wu, Dian
- Rossi, Riccardo
- Vicentini, Filippo
- Astrakhantsev, Nikita
- Becca, Federico
- Cao, Xiaodong
- Carrasquilla, Juan
- Ferrari, Francesco
- Georges, Antoine
- Hibat-Allah, Mohamed
- Imada, Masatoshi
- Läuchli, Andreas M.
- Mazzola, Guglielmo
- Mezzacapo, Antonio
- Millis, Andrew
- Robledo Moreno, Javier
- Neupert, Titus
- Nomura, Yusuke
- Nys, Jannes
- Parcollet, Olivier
- Pohle, Rico
- Romero, Imelda
- Schmid, Michael
- Silvester, J. Maxwell
- Sorella, Sandro
- Tocchio, Luca F.
- Wang, Lei
- White, Steven R.
- Wietek, Alexander
- Yang, Qi
- Yang, Yiqi
- Zhang, Shiwei
- Carleo, Giuseppe
- Venue
- Science
- Published
- 2024-10-18
- Volume
- 386
- Issue
- 6719
- Pages
- 296-301
- ISSN
- 0036-8075 (ISSN-L)
- 1095-9203
- OpenAlex
- W4403511026
- Cited by
- 79
- References
- 146
- Citations by year
- 2026: 22 · 2025: 38 · 2024: 10 · 2023: 9
- FWCI
- 10.33
- Type
- journal article
- Language
- en
- Open access
- green
- www.zora.uzh.ch
- Licence
- cc-by-nc-nd
- Locations
- Science (publishedVersion)
- PubMed (publishedVersion)
- Zurich Open Repository and Archive (University of Zurich) (acceptedVersion, cc-by-nc-nd)
- HAL (submittedVersion)
- arXiv (Cornell University) (submittedVersion)
- HAL (submittedVersion, other-oa)
- PORTO@Iris (submittedVersion, other-oa)
- ArTS Archivio della ricerca di Trieste (University of Trieste https://www.units.it/) (submittedVersion)
- DORA PSI (Paul Scherrer Institute) (submittedVersion)
- Infoscience (Ecole Polytechnique Fédérale de Lausanne) (submittedVersion, cc-by-nc-nd)
- SDL (submittedVersion)
- Zurich Open Repository and Archive (University of Zurich) (submittedVersion)
- arXiv (Cornell University)
- Zurich Open Repository and Archive (University of Zurich)
- Funders
- National Science Foundation (2110041, 205602)
- Simons Foundation
- Canadian Institute for Advanced Research
- Compute Canada
- Flatiron Health
- Government of Canada
- Deutsche Forschungsgemeinschaft (509755282, WI 5899/1-1)
- Ministry of Education, Culture, Sports, Science and Technology (JPMJPF2221, hp210163, hp220166, JPMXP1020230411, JP19H00658, JPMXP1020200104, JP22H05114, JP22H05111)
- Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung (200336, 205602, 203455, 176877)
- National Natural Science Foundation of China (92270107, 12188101)
- Institut Périmètre de physique théorique
- Ministry of Colleges and Universities
- Natural Sciences and Engineering Research Council of Canada
- Japan Society for the Promotion of Science (JP23H04869, 23H04869, JP22H05114, JP23H04519, 23K03307, JP22H05111)
- RIKEN (hp210163, JPMXP1020200104, JPMXP1020230411, hp220166)
- National Center of Competence in Research Materials’ Revolution: Computational Design and Discovery of Novel Materials (205602)
- Division of Materials Research
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Advanced Chemical Physics Studies
- Keywords
- variational energy, energy variance, benchmark dataset, variational quantum algorithms, quantum advantage, variational quantum eigensolver, quantum computing
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