Krylov diagonalization of large many-body Hamiltonians on a quantum processor

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 and Antonio Mezzacapo
Additional contact information
Nobuyuki Yoshioka: University of Tokyo
Mirko Amico: IBM Quantum T. J. Watson Research Center
William Kirby: IBM Quantum T. J. Watson Research Center
Petar Jurcevic: IBM Quantum T. J. Watson Research Center
Arkopal Dutt: IBM Quantum IBM Research Cambridge
Bryce Fuller: IBM Quantum T. J. Watson Research Center
Shelly Garion: Haifa University Campus
Holger Haas: IBM Quantum T. J. Watson Research Center
Ikko Hamamura: IBM Quantum IBM Japan 19-21 Nihonbashi Hakozaki-cho
Alexander Ivrii: Haifa University Campus
Ritajit Majumdar: IBM Quantum IBM India Research Lab
Zlatko Minev: IBM Quantum T. J. Watson Research Center
Mario Motta: IBM Quantum T. J. Watson Research Center
Bibek Pokharel: IBM Quantum IBM Research Almaden
Pedro Rivero: IBM Quantum T. J. Watson Research Center
Kunal Sharma: IBM Quantum T. J. Watson Research Center
Christopher J. Wood: IBM Quantum T. J. Watson Research Center
Ali Javadi-Abhari: IBM Quantum T. J. Watson Research Center
Antonio Mezzacapo: IBM Quantum T. J. Watson Research Center

Nature Communications, 2025, vol. 16, issue 1, 1-8

Abstract: 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.

Date: 2025
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DOI: 10.1038/s41467-025-59716-z

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