Geometric Operator Quantum Speed Limit, Wegner Hamiltonian Flow and Operator Growth
Quantum Physics
2023-07-12 v2 Statistical Mechanics
High Energy Physics - Theory
Mathematical Physics
math.MP
Abstract
Quantum speed limits (QSLs) provide lower bounds on the minimum time required for a process to unfold by using a distance between quantum states and identifying the speed of evolution or an upper bound to it. We introduce a generalization of QSL to characterize the evolution of a general operator when conjugated by a unitary. The resulting operator QSL (OQSL) admits a geometric interpretation, is shown to be tight, and holds for operator flows induced by arbitrary unitaries, i.e., with time- or parameter-dependent generators. The derived OQSL is applied to the Wegner flow equations in Hamiltonian renormalization group theory and the operator growth quantified by the Krylov complexity.
Cite
@article{arxiv.2301.04372,
title = {Geometric Operator Quantum Speed Limit, Wegner Hamiltonian Flow and Operator Growth},
author = {Niklas Hörnedal and Nicoletta Carabba and Kazutaka Takahashi and Adolfo del Campo},
journal= {arXiv preprint arXiv:2301.04372},
year = {2023}
}
Comments
33 pages, 7 figures