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.

33 pages, 7 figures

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• Operator dynamics in Lindbladian SYK: a Krylov complexity perspective
• Shortcuts to Adiabaticity in Krylov Space
• Krylov Complexity and Dynamical Phase Transition in the quenched LMG model
• 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
• Quantum Velocity Limits for Multiple Observables: Conservation Laws, Correlations, and Macroscopic Systems
• Speed limits to fluctuation dynamics
• Laser-field detuning assisted optimization of exciton valley dynamics in monolayer WSe${}_2$: Geometric quantum speed limit
• Family of attainable geometric quantum speed limits
• The exact solution of the Wegner flow equation with the Mielke generator for $3\times 3$ Hermitian matrices
• Double-Bracket Master Equations: Phase-Space Representation and Classical Limit
• Effect of measurements on quantum speed limit
• Approaching the Quantum Speed Limit in Quantum Gates with Geometric Control
• Implementation of multiparticle quantum speed limits on observables
• Krylov Complexity Under Hamiltonian Deformations and Toda Flows