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

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.

arXiv comment33 pages, 7 figures

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• Shortcuts to Adiabaticity in Krylov Space
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• Krylov complexity and Trotter transitions in unitary circuit dynamics
• Operator growth and spread complexity in open quantum systems
• Generalised quantum speed limit for arbitrary time-continuous evolution
• Universal Hypothesis of Autocorrelation Function from Krylov Complexity
• Krylov Subspace Methods for Quantum Dynamics with Time-Dependent Generators
• Fundamental speed limits on entanglement dynamics of bipartite quantum systems
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• Speed limits to fluctuation dynamics
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• Implementation of multiparticle quantum speed limits on observables
• Krylov Complexity Under Hamiltonian Deformations and Toda Flows