Shortcuts to adiabaticity: Concepts, methods, and applications

Abstract

Shortcuts to adiabaticity (STA) are fast routes to the final results of slow, adiabatic changes of the controlling parameters of a system. The shortcuts are designed by a set of analytical and numerical methods suitable for different systems and conditions. A motivation to apply STA methods to quantum systems is to manipulate them on timescales shorter than decoherence times. Thus shortcuts to adiabaticity have become instrumental in preparing and driving internal and motional states in atomic, molecular, and solid-state physics. Applications range from information transfer and processing based on gates or analog paradigms, to interferometry and metrology. The multiplicity of STA paths for the controlling parameters may be used to enhance robustness versus noise and perturbations, or to optimize relevant variables. Since adiabaticity is a widespread phenomenon, STA methods also extended beyond the quantum world, to optical devices, classical mechanical systems, and statistical physics. Shortcuts to adiabaticity combine well with other concepts and techniques, in particular with optimal control theory, and pose fundamental scientific and engineering questions such as finding speed limits, quantifying the third law, or determining process energy costs and efficiencies. We review concepts, methods and applications of shortcuts to adiabaticity and outline promising prospects, as well as open questions and challenges ahead.

Energetic cost of quantum control protocols

“…Controlling quantum systems such that an effective adiabatic dynamics is realized in a finite time can be achieved through a variety of techniques [1,2,39]. In this work, we will focus on several of the most prevalent of such protocols for a given situation and, for brevity, we refer to the comprehensive reviews on the topics for a detailed discussion of their derivations and implementations [1,2].…”

“…The inherent fragility of quantum systems necessitates that we develop methods to coherently control their evolution [1,2]. The need for high precision control is evidently ubiquitous; the study of how and why peculiar quantum properties manifest requires techniques that allows for the careful manipulation of these systems.…”

“…The need for high precision control is evidently ubiquitous; the study of how and why peculiar quantum properties manifest requires techniques that allows for the careful manipulation of these systems. While a variety of techniques have been developed for many types of quantum system [1][2][3][4], often neglected has been the associated resources needed to achieve this high degree of control. While such an omission is evidently justified when one is solely interested in studying a particular quantum phenomenon, it is vital to account for such expenditures when developing novel technologies that exploit these quantum features.…”

“…While such an omission is evidently justified when one is solely interested in studying a particular quantum phenomenon, it is vital to account for such expenditures when developing novel technologies that exploit these quantum features. Indeed, recently the application of control techniques that can achieve an effective adiabatic dynamics in a finite time, called 'shortcuts-to-adiabaticity' [1,2], has been shown to be highly effective in a diverse range of settings including quantum gates [5], quantum games [6,7] nano-scale thermodynamic cycles [8][9][10][11][12], open quantum systems [13][14][15][16], manipulating critical many-body systems [17,18], and quantum precision measurements [19]. This further highlights the importance of understanding the additional resources required to achieve precise control in a quantitative manner.…”

“…Here we choose the target state fidelity,  y t = á Yñ  | ( )| | 1 2 , where y t ñ | ( ) is the evolved state of our system using a particular control protocol and Yñ | is the target state we are aiming to achieve. By fixing the quantifier of cost and examining the paradigmatic settings of the Landau-Zener model, which serves to elucidate the control needs of critical many-body systems [17], the parametric quantum harmonic oscillator, and the Jaynes-Cummings model, we show that a consistent hierarchy of costs can emerge.…”