Optimal Control for Open Quantum Systems: Qubits and Quantum Gates

This article provides a review of recent developments in the formulation and execution of optimal control strategies for the dynamics of quantum systems. A brief introduction to the concept of optimal control, the dynamics of of open quantum systems, and quantum information processing is followed by a presentation of recent developments regarding the two main tasks in this context: state-specific and state-independent optimal control. For the former, we present an extension of conventional theory (Pontryagin's principle) to quantum systems which undergo a non-Markovian time-evolution. Owing to its importance for the realization of quantum information processing, the main body of the review, however, is devoted to state-independent optimal control. Here, we address three different approaches: an approach which treats dissipative effects from the environment in lowest-order perturbation theory, a general method based on the time--evolution superoperator concept, as well as one based on the Kraus representation of the time-evolution superoperator. Applications which illustrate these new methods focus on single and double qubits (quantum gates) whereby the environment is modeled either within the Lindblad equation or a bath of bosons (spin-boson model). While these approaches are widely applicable, we shall focus our attention to solid-state based physical realizations, such as semiconductor- and superconductor-based systems. While an attempt is made to reference relevant and representative work throughout the community, the exposition will focus mainly on work which has emerged from our own group.Comment: 27 pages, 18 figure

Validation of the Velocity Optimization for a Ropeway Passing over a Support

In this paper, we present a successful experimental validation of the velocity optimization for a cable car passing over a support. We apply the theoretical strategy developed in a previous work, refined by taking into account in a simple manner the hauling cable dynamics. The experiments at the ropeway Postal–Verano (South Tirol, Italy) have shown a significant reduction of the pendulum angle amplitude for both the descent and the ascending rides, as predicted from simulations. Furthermore, we measured a smoother progress of the torque at the driving engine during the vehicle support crossings