Geometric Operator Quantum Speed Limit, Wegner Hamiltonian Flow and Operator Growth

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 wh...

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Bibliographic Details
Published in:arXiv.org 2023-07
Main Authors: Hörnedal, Niklas, Carabba, Nicoletta, Takahashi, Kazutaka, Adolfo del Campo
Format: Article
Language:English
Subjects:
Evolution
Flow equations
Group theory
Lower bounds
Speed limits
Upper bounds
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2301.04372