Common Foundations of Optimal Control Across the Sciences: evidence of a free lunch

Abstract

A common goal in the sciences is optimization of an objective function by selecting control variables such that a desired outcome is achieved. This scenario can be expressed in terms of a control landscape of an objective considered as a function of the control variables. At the most basic level, it is known that the vast majority of quantum control landscapes possess no traps, whose presence would hinder reaching the objective. This paper reviews and extends the quantum control landscape assessment, presenting evidence that the same highly favorable landscape features exist in many other domains of science. The implications of this broader evidence are discussed. Specifically, control landscape examples from quantum mechanics, chemistry, and evolutionary biology are presented. Despite the obvious differences, commonalities between these areas are highlighted within a unified mathematical framework. This mathematical framework is driven by the wide ranging experimental evidence on the ease of finding optimal controls (in terms of the required algorithmic search effort beyond laboratory set up overhead). The full scope and implications of this observed common control behavior pose an open question for assessment in further work.

arXiv comment2 figures, proceedings of the royal society A, 2016

References in corpus (16)

• Quantum control theory and applications: A survey
• Controllability of quantum mechanical systems by root space decomposition of su(N)
• Quantum Control Landscapes
• Are there traps in quantum control landscapes?
• Exploring constrained quantum control landscapes
• Quantum Control Landscapes: A Closer Look
• Control Landscapes for Observable Preparation with Open Quantum Systems
• Singularities of Quantum Control Landscapes
• Search complexity and resource scaling for the quantum optimal control of unitary transformations
• Control of open quantum systems: Case study of the central spin model
• Searching for quantum optimal controls in the presence of singular critical points
• Comment on "Are There Traps in Quantum Control Landscapes?"
• Searching for quantum optimal controls under severe constraints
• Experimental exploration over a quantum control landscape through nuclear magnetic resonance
• Role of control constraints in quantum optimal control
• Dynamic Homotopy and Landscape Dynamical Set Topology in Quantum Control

Cited by in corpus (5)

• Machine learning \& artificial intelligence in the quantum domain
• Quantum optimal control using phase-modulated driving fields
• Comment on "Control landscapes are almost always trap free: a geometric assessment"
• Constraint optimization and $\mathcal{S}\mathcal{U}(N)$ quantum control landscapes
• Coherent dynamical control of quantum processes