Hybrid optimization schemes for quantum control

Optimal control theory is a powerful tool for solving control problems in quantum mechanics, ranging from the control of chemical reactions to the implementation of gates in a quantum computer. Gradient-based optimization methods are able to find high fidelity controls, but require considerable numerical effort and often yield highly complex solutions. We propose here to employ a two-stage optimization scheme to significantly speed up convergence and achieve simpler controls. The control is initially parametrized using only a few free parameters, such that optimization in this pruned search space can be performed with a simplex method. The result, considered now simply as an arbitrary function on a time grid, is the starting point for further optimization with a gradient-based method that can quickly converge to high fidelities. We illustrate the success of this hybrid technique by optimizing a geometric phase gate for two superconducting transmon qubits coupled with a shared transmission line resonator, showing that a combination of Nelder-Mead simplex and Krotov’s method yields considerably better results than either one of the two methods alone.

Multi-Scale Governance of Sustainable Natural Resource Use—Challenges and Opportunities for Monitoring and Institutional Development at the National and Global Level

In a globalized economy, the use of natural resources is determined by the demand of modern production and consumption systems, and by infrastructure development. Sustainable natural resource use will require good governance and management based on sound scientific information, data and indicators. There is a rich literature on natural resource management, yet the national and global scale and macro-economic policy making has been underrepresented. We provide an overview of the scholarly literature on multi-scale governance of natural resources, focusing on the information required by relevant actors from local to global scale. Global natural resource use is largely determined by national, regional, and local policies. We observe that in recent decades, the development of public policies of natural resource use has been fostered by an “inspiration cycle” between the research, policy and statistics community, fostering social learning. Effective natural resource policies require adequate monitoring tools, in particular indicators for the use of materials, energy, land, and water as well as waste and GHG emissions of national economies. We summarize the state-of-the-art of the application of accounting methods and data sources for national material flow accounts and indicators, including territorial and product-life-cycle based approaches. We show how accounts on natural resource use can inform the Sustainable Development Goals (SDGs) and argue that information on natural resource use, and in particular footprint indicators, will be indispensable for a consistent implementation of the SDGs. We recognize that improving the knowledge base for global natural resource use will require further institutional development including at national and international levels, for which we outline options.