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 distance between quantum states and identifying of evolution or an upper bound it. We introduce generalization QSL characterize general operator when conjugated unitary. The resulting (OQSL) admits geometric interpretation, is shown be tight, holds flows induced arbitrary unitaries, i.e., with time- parameter-dependent generators. derived OQSL applied Wegner flow equations in Hamiltonian renormalization group theory growth quantified Krylov complexity.