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DOE OSTI · 3380414

Krylov Subspace Methods for Quantum Dynamics with Time-Dependent Generators

Takahashi, Kazutaka [University of Luxembourg (Luxembourg); Mie University (Japan)] (ORCID:0000000173212571)·del Campo Echevarria, Adolfo [University of Luxembourg (Luxembourg); Donostia International Physics Center (DIPC), San Sebastian (Spain); Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)] (ORCID:0000000322192851)
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Abstract

Krylov subspace methods in quantum dynamics identify the minimal subspace in which a process unfolds. To date, their use is restricted to time evolutions governed by time-independent generators. Here, we introduce a generalization valid for driven quantum systems governed by a time-dependent Hamiltonian that maps the evolution to a diffusion problem in a one-dimensional lattice with nearest-neighbor hopping probabilities that are inhomogeneous and time dependent. This representation is used to establish a novel class of fundamental limits to the quantum speed of evolution and operator growth. We also discuss generalizations of the algorithm, adapted to discretized time evolutions and periodic Hamiltonians, with applications to many-body systems.

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71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

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Takahashi, Kazutaka [University of Luxembourg (Luxembourg); Mie University (Japan)] (ORCID:0000000173212571), del Campo Echevarria, Adolfo [University of Luxembourg (Luxembourg); Donostia International Physics Center (DIPC), San Sebastian (Spain); Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)] (ORCID:0000000322192851). 2025-01-22. Krylov Subspace Methods for Quantum Dynamics with Time-Dependent Generators. https://doi.org/10.1103/physrevlett.134.030401

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