Krylov Subspace Methods for Quantum Dynamics with Time-Dependent Generators

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.

6+15 pages, 3+1 figures

References in corpus (4)

• The Magnus expansion and some of its applications
• Krylov complexity of density matrix operators
• Krylov Complexity and Dynamical Phase Transition in the quenched LMG model
• Spread complexity and quantum chaos for periodically driven spin chains

Cited by in corpus (7)

• Quantum Dynamics in Krylov Space: Methods and Applications
• Quantum complexity in gravity, quantum field theory, and quantum information science
• Correlations and Krylov spread for a non-Hermitian Hamiltonian: Ising chain with a complex-valued transverse magnetic field
• Phase transitions in a non-Hermitian Su-Schrieffer-Heeger model via Krylov spread complexity
• Dynamical quantum phase transition, metastable state, and dimensionality reduction: Krylov analysis of fully connected spin models
• Implementation of multiparticle quantum speed limits on observables
• Krylov Complexity Under Hamiltonian Deformations and Toda Flows