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Certificates of quantum many-body properties assisted by machine learning

Borja Requena1, Gorka Muñoz-Gil1,2, Maciej Lewenstein1,3, Vedran Dunjko4, and Jordi Tura5,6,*

  • 1ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Av. Carl Friedrich Gauss 3, 08860 Castelldefels (Barcelona), Spain
  • 2Institute for Theoretical Physics, University of Innsbruck, Technikerstr. 21a, A-6020 Innsbruck, Austria
  • 3ICREA, Pg. Lluís Companys 23, 08010 Barcelona, Spain
  • 4LIACS, Leiden University, Niels Bohrweg 1, 2333 CA Leiden, The Netherlands
  • 5Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, 85748 Garching, Germany
  • 6Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands

  • *Corresponding author: tura@lorentz.leidenuniv.nl

Rigorous Anderson-type lower bounds on the ground-state energy of the pyrochlore Heisenberg antiferromagnet

Péter Kránitz and Karlo Penc

Zeitschrift für Naturforschung A 81 373 (2026)

Scalable ground-state certification of quantum spin systems via structured noncommutative polynomial optimization

Jie Wang, David Jansen, Irénée Frerot, Marc-Olivier Renou, Victor Magron, and Antonio Acín

SciPost Phys. 21 074 (2026)

Mapping Phase Diagrams of Quantum Spin Systems through Semidefinite-Programming Relaxations

David Jansen, Donato Farina, Luke Mortimer, Timothy Heightman, Andreas Leitherer, Pere Mujal, Jie Wang, and Antonio Acín

Phys. Rev. Lett. 136 050401 (2026)

Characterizing translation-invariant Bell inequalities using tropical algebra and graph polytopes

Mengyao Hu, Eloïc Vallée, Tim Seynnaeve, Patrick Emonts, Fatemeh Mohammadi, and Jordi Tura

Phys. Rev. A 113 032421 (2026)

First-Order Optimality Conditions for Non-Commutative Optimization Problems

Mateus Araújo, Igor Klep, Andrew J. P. Garner, Tamás Vértesi, and Miguel Navascués

Found Comput Math (2026)

Supervised learning of the Jaynes–Cummings Hamiltonian

Woohyun Choi, Chang-Woo Lee, and Changsuk Noh

Sci Rep 15 27556 (2025)

Certifying steady-state properties of open quantum systems

Luke Mortimer, Donato Farina, Grazia Di Bello, David Jansen, Andreas Leitherer, Pere Mujal, and Antonio Acín

Phys. Rev. Research 7 033237 (2025)

Mitigating shot noise in local overlapping quantum tomography with semidefinite programming

Zherui Jerry Wang, David Dechant, Yash J. Patel, and Jordi Tura

Phys. Rev. A 111 052444 (2025)

Machine learning approach to reconstruct density matrices from quantum marginals

Daniel Uzcategui-Contreras, Antonio Guerra, Sebastian Niklitschek, and Aldo Delgado

Mach. Learn.: Sci. Technol. 6 025068 (2025)

Machine Learning of Two-Electron Reduced Density Matrices for Many-Body Problems

Luis H. Delgado-Granados, LeeAnn M. Sager-Smith, Kristina Trifonova, and David A. Mazziotti

J. Phys. Chem. Lett. 16 2231 (2025)

Certifying Ground-State Properties of Many-Body Systems

Jie Wang, Jacopo Surace, Irénée Frérot, Benoît Legat, Marc-Olivier Renou, Victor Magron, and Antonio Acín

Phys. Rev. X 14 031006 (2024)

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