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

Niklas Hörnedal¹, Nicoletta Carabba¹, Kazutaka Takahashi^1,2, and Adolfo del Campo^1,3

¹Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, G. D. Luxembourg
²Department of Physics Engineering, Faculty of Engineering, Mie University, Mie 514–8507, Japan
³Donostia International Physics Center, E-20018 San Sebastián, Spain

Published:	2023-07-11, volume 7, page 1055
Eprint:	arXiv:2301.04372v2
Doi:	https://doi.org/10.22331/q-2023-07-11-1055
Citation:	Quantum 7, 1055 (2023).

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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.

► BibTeX data

@article{Hornedal2023geometricoperator,
  doi = {10.22331/q-2023-07-11-1055},
  url = {https://doi.org/10.22331/q-2023-07-11-1055},
  title = {Geometric {O}perator {Q}uantum {S}peed {L}imit, {W}egner {H}amiltonian {F}low and {O}perator {G}rowth},
  author = {H{\"{o}}rnedal, Niklas and Carabba, Nicoletta and Takahashi, Kazutaka and del Campo, Adolfo},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {7},
  pages = {1055},
  month = jul,
  year = {2023}
}

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