RESUMEN
Adiabatic time evolution can be used to prepare a complicated quantum many-body state from one that is easier to synthesize and Trotterization can be used to implement such an evolution digitally. The complex interplay between nonadiabaticity and digitization influences the infidelity of this process. We prove that the first-order Trotterization of a complete adiabatic evolution has a cumulative infidelity that scales as O(T^{-2}δt^{2}) instead of O(T^{2}δt^{2}) expected from general Trotter error bounds, where δt is the time step and T is the total time. This result suggests a self-healing mechanism and explains why, despite increasing T, infidelities for fixed-δt digitized evolutions still decrease for a wide variety of Hamiltonians. It also establishes a correspondence between the quantum approximate optimization algorithm and digitized quantum annealing.
RESUMEN
It is hoped that quantum computers will offer advantages over classical computers for combinatorial optimization. Here, we introduce a feedback-based strategy for quantum optimization, where the results of qubit measurements are used to constructively assign values to quantum circuit parameters. We show that this procedure results in an estimate of the combinatorial optimization problem solution that improves monotonically with the depth of the quantum circuit. Importantly, the measurement-based feedback enables approximate solutions to the combinatorial optimization problem without the need for any classical optimization effort, as would be required for the quantum approximate optimization algorithm. We demonstrate this feedback-based protocol on a superconducting quantum processor for the graph-partitioning problem MaxCut, and present a series of numerical analyses that further investigate the protocol's performance.
RESUMEN
Mobile health (mHealth) technologies are contributing to the increasing relevance of control engineering principles in understanding and improving health behaviors, such as physical activity. Social Cognitive Theory (SCT), one of the most influential theories of health behavior, has been used as the conceptual basis for behavioral interventions for smoking cessation, weight management, and other health-related outcomes. This paper presents a control-oriented dynamical systems model of SCT based on fluid analogies that can be used in system identification and control design problems relevant to the design and analysis of intensively adaptive interventions. Following model development, a series of simulation scenarios illustrating the basic workings of the model are presented. The model's usefulness is demonstrated in the solution of two important practical problems: 1) semiphysical model estimation from data gathered in a physical activity intervention (the MILES study) and 2) as a means for discerning the range of "ambitious but doable" daily step goals in a closed-loop behavioral intervention aimed at sedentary adults. The model is the basis for ongoing experimental validation efforts, and should encourage additional research in applying control engineering technologies to the social and behavioral sciences.
RESUMEN
We perform quantum optimal control simulations, based on the Time-Dependent Hartree (TDH) approximation, for systems of three to five dipole-dipole coupled OCS rotors. A control electric field is used to steer all of the individual rotors, arranged in chains and regular polygons in a plane, toward either identical or unique objectives. The goal is to explore the utility of the TDH approximation to model the field-induced dynamics of multiple interacting rotors in the weak dipole-dipole coupling regime. A stochastic hill climbing approach is employed to seek an optimal control field that achieves the desired objectives at a specified target time. We first show that multiple rotors in chain and polygon geometries can be identically oriented in the same direction; these cases do not significantly depend on the presence of the dipole-dipole interaction. Additionally, in particular geometrical arrangements, we demonstrate that individual rotors can be uniquely manipulated toward different objectives with the same field. Specifically, it is shown that for a three rotor chain, the two end rotors can be identically oriented in a specific direction while keeping the middle rotor in its ground state, and for an equilateral triangle, two rotors can be identically oriented in a specific direction while the third rotor is oriented in the opposite direction. These multirotor unique objective cases exploit the shape of the field in coordination with dipole-dipole coupling between the rotors. Comparisons to numerically exact calculations, utilizing the TDH-determined fields, are given for all optimal control studies involving systems of three rotors.