Krylov Subspace Methods for Quantum Dynamics with Time-Dependent Generators

• URL: http://arxiv.org/abs/2408.08383v1
• Date: Thu, 15 Aug 2024 19:00:24 GMT
• Title: Krylov Subspace Methods for Quantum Dynamics with Time-Dependent Generators
• Authors: Kazutaka Takahashi, Adolfo del Campo,
• Abstract summary: We introduce a generalization valid for driven quantum systems governed by a time-dependent Hamiltonian. 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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. 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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