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

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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

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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}<br /> }

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Cited by

[1] Dimitrios Patramanis and Watse Sybesma, “Krylov complexity in a natural basis for the Schrödinger algebra”, arXiv:2306.03133, (2023).

[2] Ryusuke Hamazaki, “Quantum Velocity Limits for Multiple Observables: Conservation Laws, Correlations, and Macroscopic Systems”, arXiv:2305.03190, (2023).

[3] Pawel Caputa, Javier M. Magan, Dimitrios Patramanis, and Erik Tonni, “Krylov complexity of modular Hamiltonian evolution”, arXiv:2306.14732, (2023).

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