Krylov diagonalization of large many-body Hamiltonians on a quantum processor
Abstract The estimation of low energies of many-body systems is a cornerstone of the computational quantum sciences. Variational quantum algorithms can be used to prepare ground states on pre-fault-tolerant quantum processors, but their lack of convergence guarantees and impractical number of cost f...
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2025-06-01
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| Series: | Nature Communications |
| Online Access: | https://doi.org/10.1038/s41467-025-59716-z |
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| author | Nobuyuki Yoshioka Mirko Amico William Kirby Petar Jurcevic Arkopal Dutt Bryce Fuller Shelly Garion Holger Haas Ikko Hamamura Alexander Ivrii Ritajit Majumdar Zlatko Minev Mario Motta Bibek Pokharel Pedro Rivero Kunal Sharma Christopher J. Wood Ali Javadi-Abhari Antonio Mezzacapo |
| author_facet | Nobuyuki Yoshioka Mirko Amico William Kirby Petar Jurcevic Arkopal Dutt Bryce Fuller Shelly Garion Holger Haas Ikko Hamamura Alexander Ivrii Ritajit Majumdar Zlatko Minev Mario Motta Bibek Pokharel Pedro Rivero Kunal Sharma Christopher J. Wood Ali Javadi-Abhari Antonio Mezzacapo |
| author_sort | Nobuyuki Yoshioka |
| collection | DOAJ |
| description | Abstract The estimation of low energies of many-body systems is a cornerstone of the computational quantum sciences. Variational quantum algorithms can be used to prepare ground states on pre-fault-tolerant quantum processors, but their lack of convergence guarantees and impractical number of cost function estimations prevent systematic scaling of experiments to large systems. Alternatives to variational approaches are needed for large-scale experiments on pre-fault-tolerant devices. Here, we use a superconducting quantum processor to compute eigenenergies of quantum many-body systems on two-dimensional lattices of up to 56 sites, using the Krylov quantum diagonalization algorithm, an analog of the well-known classical diagonalization technique. We construct subspaces of the many-body Hilbert space using Trotterized unitary evolutions executed on the quantum processor, and classically diagonalize many-body interacting Hamiltonians within those subspaces. These experiments demonstrate exponential convergence towards an estimate of the ground state energy, and show that quantum diagonalization algorithms are poised to complement their classical counterparts at the foundation of computational methods for quantum systems. |
| format | Article |
| id | doaj-art-679fffd2bb6e4f5ea74f3b37f19adb11 |
| institution | Matheson Library |
| issn | 2041-1723 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Nature Communications |
| spelling | doaj-art-679fffd2bb6e4f5ea74f3b37f19adb112025-06-29T11:13:18ZengNature PortfolioNature Communications2041-17232025-06-011611810.1038/s41467-025-59716-zKrylov diagonalization of large many-body Hamiltonians on a quantum processorNobuyuki Yoshioka0Mirko Amico1William Kirby2Petar Jurcevic3Arkopal Dutt4Bryce Fuller5Shelly Garion6Holger Haas7Ikko Hamamura8Alexander Ivrii9Ritajit Majumdar10Zlatko Minev11Mario Motta12Bibek Pokharel13Pedro Rivero14Kunal Sharma15Christopher J. Wood16Ali Javadi-Abhari17Antonio Mezzacapo18Department of Applied Physics, University of TokyoIBM Quantum T. J. Watson Research CenterIBM Quantum T. J. Watson Research CenterIBM Quantum T. J. Watson Research CenterIBM Quantum IBM Research CambridgeIBM Quantum T. J. Watson Research CenterIBM Quantum, IBM Research Israel, Haifa University CampusIBM Quantum T. J. Watson Research CenterIBM Quantum IBM Japan 19-21 Nihonbashi Hakozaki-choIBM Quantum, IBM Research Israel, Haifa University CampusIBM Quantum IBM India Research LabIBM Quantum T. J. Watson Research CenterIBM Quantum T. J. Watson Research CenterIBM Quantum IBM Research AlmadenIBM Quantum T. J. Watson Research CenterIBM Quantum T. J. Watson Research CenterIBM Quantum T. J. Watson Research CenterIBM Quantum T. J. Watson Research CenterIBM Quantum T. J. Watson Research CenterAbstract The estimation of low energies of many-body systems is a cornerstone of the computational quantum sciences. Variational quantum algorithms can be used to prepare ground states on pre-fault-tolerant quantum processors, but their lack of convergence guarantees and impractical number of cost function estimations prevent systematic scaling of experiments to large systems. Alternatives to variational approaches are needed for large-scale experiments on pre-fault-tolerant devices. Here, we use a superconducting quantum processor to compute eigenenergies of quantum many-body systems on two-dimensional lattices of up to 56 sites, using the Krylov quantum diagonalization algorithm, an analog of the well-known classical diagonalization technique. We construct subspaces of the many-body Hilbert space using Trotterized unitary evolutions executed on the quantum processor, and classically diagonalize many-body interacting Hamiltonians within those subspaces. These experiments demonstrate exponential convergence towards an estimate of the ground state energy, and show that quantum diagonalization algorithms are poised to complement their classical counterparts at the foundation of computational methods for quantum systems.https://doi.org/10.1038/s41467-025-59716-z |
| spellingShingle | Nobuyuki Yoshioka Mirko Amico William Kirby Petar Jurcevic Arkopal Dutt Bryce Fuller Shelly Garion Holger Haas Ikko Hamamura Alexander Ivrii Ritajit Majumdar Zlatko Minev Mario Motta Bibek Pokharel Pedro Rivero Kunal Sharma Christopher J. Wood Ali Javadi-Abhari Antonio Mezzacapo Krylov diagonalization of large many-body Hamiltonians on a quantum processor Nature Communications |
| title | Krylov diagonalization of large many-body Hamiltonians on a quantum processor |
| title_full | Krylov diagonalization of large many-body Hamiltonians on a quantum processor |
| title_fullStr | Krylov diagonalization of large many-body Hamiltonians on a quantum processor |
| title_full_unstemmed | Krylov diagonalization of large many-body Hamiltonians on a quantum processor |
| title_short | Krylov diagonalization of large many-body Hamiltonians on a quantum processor |
| title_sort | krylov diagonalization of large many body hamiltonians on a quantum processor |
| url | https://doi.org/10.1038/s41467-025-59716-z |
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