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

• URL: http://arxiv.org/abs/2301.04372v2
• Date: Thu, 22 Jun 2023 09:43:58 GMT
• Title: Geometric Operator Quantum Speed Limit, Wegner Hamiltonian Flow and Operator Growth
• Authors: Niklas H\"ornedal, Nicoletta Carabba, Kazutaka Takahashi, Adolfo del Campo
• Abstract summary: Quantum speed limits (QSLs) provide lower bounds on the minimum time required for a process to unfold. We introduce a generalization of QSL to characterize the evolution of a general operator whenconjugated 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. The derived OQSL is applied to the Wegner flow equations in Hamiltonian renormalization group theory and the operator growth quantified by the Krylov complexity.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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