Abstract
We quantitatively assess the energetic cost of several well-known control protocols that achieve a finite time adiabatic dynamics, namely counterdiabatic and local counterdiabatic driving, optimal control, and inverse engineering. By employing a cost measure based on the norm of the total driving Hamiltonian, we show that a hierarchy of costs emerges that is dependent on the protocol duration. As case studies we explore the Landau–Zener model, the quantum harmonic oscillator, and the Jaynes–Cummings model and establish that qualitatively similar results hold in all cases. For the analytically tractable Landau–Zener case, we further relate the effectiveness of a control protocol with the spectral features of the new driving Hamiltonians and show that in the case of counterdiabatic driving, it is possible to further minimize the cost by optimizing the ramp.
Highlights
The inherent fragility of quantum systems necessitates that we develop methods to coherently control their evolution [1, 2]
These differences are very sensitive to the total protocol duration, as shown in Fig. 1(d)-(f) where we we show the same quantities for τ = 0.1
For the Landau-Zener model, we have shown that optimal control protocols appear to be the most efficient techniques and presented a remarkable invariance to the protocol duration
Summary
The inherent fragility of quantum systems necessitates that we develop methods to coherently control their evolution [1, 2]. Recently the application of control techniques that can achieve an effective adiabatic dynamics in a finite time, called “shortcutsto-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]. IV we draw our conclusions and provide some further discussions
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