Abstract :
[en] 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.
Funding text :
We thank Budhaditya Bhattacharjee, Andres Grabarits, Aritra Kundu, Pratik Nandy, and Ruth Shir for stimulating discussions. A. dC. thanks the Los Alamos National Laboratory for its hospitality during the completion of this work. We acknowledge the financial support from the Luxembourg National Research Fund (FNR Grant No. 16434093). This project has received funding from the QuantERA II Joint Programme with co-funding from the European Union's Horizon 2020 research and innovation programme. K.T. further acknowledges support from JSPS KAKENHI Grant No. JP24K00547.We thank Budhaditya Bhattacharjee, Andr\u00E1s Grabarits, Aritra Kundu, Pratik Nandy, and Ruth Shir for stimulating discussions. A. dC. thanks the Los Alamos National Laboratory for its hospitality during the completion of this work. We acknowledge the financial support from the Luxembourg National Research Fund (FNR Grant No. 16434093). This project has received funding from the QuantERA II Joint Programme with co-funding from the European Union\u2019s Horizon 2020 research and innovation programme. K.\u2009T. further acknowledges support from JSPS KAKENHI Grant No. JP24K00547.
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