RESUMO
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.
RESUMO
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.
RESUMO
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.
