Unified formulation for control and inversion of molecular dynamics

Abstract

In this paper we present a unified approach for the control and inversion of molecular dynamics. The concept of molecular tracking ties the subjects to a common formulation. For molecular control the time-dependent track of an observable operator is imposed a priori and the control field is determined to meet the track. For extraction of the potential and/or dipole function the time-dependent track is observed laboratory data. A common three-step algorithm is presented to treat both seemingly unrelated problems. The essential features of the algorithm are presented in the paper.

Implicit Lyapunov control of finite dimensional Schrödinger equations

“…Simulating the closedloop system, we obtain a control signal which can be used in open-loop for the physical system. Such kind of strategy has already been applied widely in this framework [5,13,22,18].…”

Reference Trajectory Tracking for Locally Designed Coherent Quantum Controls

“…[1][2][3][4]11,13,35 Very often, control of quantum phenomena is expressed as the minimization of a setting-dependent cost functional that describes the goal to be attained and the eventual penalties to consider. Three types of generic minimization procedures have been used in the literature: stochastic iterative approaches (e.g., genetic algorithms), 7,15 iterative critical point methods that use adjoint state information and give rise to monotonic algorithms, 10,17,29,32,36 and tracking or local control procedures 6,8,12,16,20,30,31 that obtain explicitly the control field from the prescribed trajectory that the system is required to take (and devise additional techniques to avoid eventual singularities). The advantage of this last class of methods is that it only requires one (or few) propagations of the time-dependent Schrödinger equation (TDSE); when larger systems are to be treated, this property may prove crucial for the numerical tractability of the simulations.…”

Stabilizing qubit coherence via tracking-control

“…Tracking-control has a rich history in classical control theory [8,9,10,11,12]. It was extensively studied by Rabitz and co-workers in the context of closed quantum systems (specifically, molecular systems) [13,14,15,16,17,18]. Here it refers to the instantaneous adjustment of the control field based on a continuous measurement of the state of the qubit.…”