Abstract
Optimization is ubiquitous in the control of quantum dynamics in atomic, molecular, and optical systems. The ease or difficulty of finding control solutions, which is practically crucial for developing quantum technologies, is highly dependent on the geometry of the underlying optimization landscapes. In this review, we give an introduction to the basic concepts in the theory of quantum optimal control landscapes, and their trap-free critical topology under two fundamental assumptions. Furthermore, the effects of various factors on the search effort are discussed, including control constraints, singularities, saddles, noises, and non-topological features of the landscapes. Additionally, we review recent experimental advances in the control of molecular and spin systems. These results provide an overall understanding of the optimization complexity of quantum control dynamics, which may help to develop more efficient optimization algorithms for quantum control systems, and as a promising extension, the training processes in quantum machine learning.
Highlights
Over the past decades, the development of quantum technologies has garnered much attention for their vast potential applications to computation, communication, and metrology[1]
From the viewpoint of quantum physics, the design of open-loop quantum control is usually taken as an inverse problem of input-output analysis, which has successfully produced many methods such as stimulated Raman adiabatic passage (STIRAP) for resilience to control noises[5] and dynamical decoupling (DD) for robustness to decoherence noises[6] in quantum information sciences
We will first show that, under some universal assumptions that need to be satisfied in practice, the quantum optimal control landscapes are devoid of local traps, i.e., the search for optimal controls starting from any initial guess will eventually reach a global optimal solution without being stopped by local suboptimal solutions
Summary
The development of quantum technologies has garnered much attention for their vast potential applications to computation, communication, and metrology[1]. We will first show that, under some universal assumptions (i.e., sufficient conditions) that need to be satisfied in practice, the quantum optimal control landscapes are devoid of local traps, i.e., the search for optimal controls starting from any initial guess will eventually reach a global optimal solution without being stopped by local suboptimal solutions. This subject addresses the fundamental topology of the landscape, and the review studies the landscape topology from various perspectives, including when the assumptions may be violated, as well as experimental exploration of quantum control landscapes in molecular and spin systems.
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