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Wu D, Rossi R, Vicentini F, Astrakhantsev N, Becca F, Cao X, Carrasquilla J, Ferrari F, Georges A, Hibat-Allah M, Imada M, Läuchli AM, Mazzola G, Mezzacapo A, Millis A, Robledo Moreno J, Neupert T, Nomura Y, Nys J, Parcollet O, Pohle R, Romero I, Schmid M, Silvester JM, Sorella S, Tocchio LF, Wang L, White SR, Wietek A, Yang Q, Yang Y, Zhang S, Carleo G. Variational benchmarks for quantum many-body problems. Science 2024; 386:296-301. [PMID: 39418373 DOI: 10.1126/science.adg9774] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/09/2023] [Accepted: 09/12/2024] [Indexed: 10/19/2024]
Abstract
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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Affiliation(s)
- Dian Wu
- Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
- Center for Quantum Science and Engineering, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Riccardo Rossi
- Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
- Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée, LPTMC, F-75005 Paris, France
| | - Filippo Vicentini
- Center for Quantum Science and Engineering, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
- CPHT, CNRS, Ecole Polytechnique, IP Paris, F-91128 Palaiseau, France
- Collège de France, 75005 Paris, France
| | | | - Federico Becca
- Dipartimento di Fisica, Università di Trieste, Strada Costiera 11, I-34151 Trieste, Italy
| | - Xiaodong Cao
- Center for Computational Quantum Physics, Flatiron Institute, New York, NY 10010, USA
| | - Juan Carrasquilla
- Vector Institute, MaRS Centre, Toronto, ON M5G 1M1, Canada
- Institute for Theoretical Physics, ETH Zürich, 8093 Zurich, Switzerland
| | - Francesco Ferrari
- Institut für Theoretische Physik, Goethe-Universit ät, 60438 Frankfurt am Main, Germany
| | - Antoine Georges
- CPHT, CNRS, Ecole Polytechnique, IP Paris, F-91128 Palaiseau, France
- Collège de France, 75005 Paris, France
- Center for Computational Quantum Physics, Flatiron Institute, New York, NY 10010, USA
- Department of Quantum Matter Physics, Université de Genève, CH-1211 Geneva, Switzerland
| | - Mohamed Hibat-Allah
- Vector Institute, MaRS Centre, Toronto, ON M5G 1M1, Canada
- Perimeter Institute for Theoretical Physics, Waterloo, ON N2L 2Y5, Canada
- Department of Physics and Astronomy, University of Waterloo, Waterloo, ON N2L 3G1, Canada
- Department of Applied Mathematics, University of Waterloo, Waterloo, ON N2L 3G1, Canada
| | - Masatoshi Imada
- Toyota Physical and Chemical Research Institute, 41-1 Yokomichi, Nagakute, Aichi, 480-1192, Japan
- Waseda Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo, 169-8555, Japan
- Physics Division, Sophia University, Chiyoda-ku, Tokyo, 102-8554, Japan
- Department of Applied Physics, University of Tokyo, Hongo, Bunkyo-ku, Tokyo, 113-8656, Japan
| | - Andreas M Läuchli
- Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
- Laboratory for Theoretical and Computational Physics, Paul Scherrer Institute, 5232 Villigen, Switzerland
| | - Guglielmo Mazzola
- Institute for Computational Science, University of Zurich, 8057 Zurich, Switzerland
| | - Antonio Mezzacapo
- IBM Quantum, T. J. Watson Research Center, Yorktown Heights, NY 10598, USA
| | - Andrew Millis
- Center for Computational Quantum Physics, Flatiron Institute, New York, NY 10010, USA
- Department of Physics, Columbia University, New York, NY 10027, USA
| | - Javier Robledo Moreno
- Center for Computational Quantum Physics, Flatiron Institute, New York, NY 10010, USA
- Center for Quantum Phenomena, Department of Physics, New York University, New York, NY 10003, USA
| | - Titus Neupert
- Department of Physics, University of Zurich, 8057 Zurich, Switzerland
| | - Yusuke Nomura
- Department of Applied Physics and Physico-Informatics, Keio University, 3-1471 Hiyoshi, Kohoku-ku, Yokohama, 223-8522, Japan
- Institute for Materials Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai, 980-8577, Japan
| | - Jannes Nys
- Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
- Center for Quantum Science and Engineering, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Olivier Parcollet
- Center for Computational Quantum Physics, Flatiron Institute, New York, NY 10010, USA
- Université Paris-Saclay, CNRS, CEA, Institut de physique théorique, 91191 Gif-sur-Yvette, France
| | - Rico Pohle
- Waseda Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo, 169-8555, Japan
- Department of Applied Physics, University of Tokyo, Hongo, Bunkyo-ku, Tokyo, 113-8656, Japan
| | - Imelda Romero
- Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
- Center for Quantum Science and Engineering, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Michael Schmid
- Waseda Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo, 169-8555, Japan
| | - J Maxwell Silvester
- Department of Physics and Astronomy, University of California, Irvine, CA 92697, USA
| | - Sandro Sorella
- SISSA, International School for Advanced Studies, 34136 Trieste, Italy
| | - Luca F Tocchio
- Institute for Condensed Matter Physics and Complex Systems, Department of Applied Science and Technology (DISAT), Politecnico di Torino, I-10129 Torino, Italy
| | - Lei Wang
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China
| | - Steven R White
- Department of Physics and Astronomy, University of California, Irvine, CA 92697, USA
| | - Alexander Wietek
- Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany
| | - Qi Yang
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- University of Chinese Academy of Sciences, Beijing 100049, China
| | - Yiqi Yang
- Department of Physics, College of William and Mary, Williamsburg, VA 23187, USA
| | - Shiwei Zhang
- Center for Computational Quantum Physics, Flatiron Institute, New York, NY 10010, USA
| | - Giuseppe Carleo
- Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
- Center for Quantum Science and Engineering, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
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