Krylov Complexity

Krylov complexity provides a powerful framework for understanding how operators and states spread across the Hilbert space of quantum systems. By studying the growth of operators in Krylov space, we gain insights into fundamental aspects of quantum chaos, thermalization, and the emergence of computational complexity in quantum many-body systems.

Our research investigates how Krylov complexity connects to holographic descriptions of quantum gravity, black hole physics, and the fundamental limits of quantum computation.

key questions

  • How does Krylov complexity relate to other measures of quantum chaos?
  • What universal features characterize operator growth in chaotic systems?
  • Can Krylov methods illuminate aspects of black hole dynamics?
  • How do integrability and chaos manifest in Krylov space?

Key Publications

  • Krylov Complexity

    E. Rabinovici, A. Sánchez-Garrido, R. Shir, J. Sonner

    arXiv:2507.06286 Preprint (2025)
  • Krylov Localization and suppression of complexity

    E. Rabinovici, A. Sánchez-Garrido, R. Shir, J. Sonner

    arXiv:2112.12128 JHEP 03 (2022) 211 (2022)
  • A bulk manifestation of Krylov complexity

    E. Rabinovici, A. Sánchez-Garrido, R. Shir, J. Sonner

    arXiv:2305.04355 JHEP 08 (2023) 213 (2023)
  • Operator K-complexity in DSSYK: Krylov complexity equals bulk length

    M. Ambrosini, E. Rabinovici, A. Sánchez-Garrido, R. Shir, J. Sonner

    arXiv:2412.15318 Preprint (2024)