Generalized shortcuts to adiabaticity and enhanced robustness against decoherence

Abstract

Shortcuts to adiabaticity provide a general approach to mimic adiabatic quantum processes via arbitrarily fast evolutions in Hilbert space. For these counterdiabatic evolutions, higher speed comes at higher energy cost. Here, the counterdiabatic theory is employed as a minimal energy demanding scheme for speeding up adiabatic tasks. As a by-product, we show that this approach can be used to obtain infinite classes of transitionless models, including time-independent Hamiltonians under certain conditions over the eigenstates of the original Hamiltonian. We apply these results to investigate shortcuts to adiabaticity in decohering environments by introducing the requirement of a fixed energy resource. In this scenario, we show that generalized transitionless evolutions can be more robust against decoherence than their adiabatic counterparts. We illustrate this enhanced robustness both for the Landau-Zener model and for quantum gate Hamiltonians.

Energetic cost of quantum control protocols

“…If one is only interested in controlling populations, then with a suitable choice of phase [30] this can be achieved through the CD term…”

“…Our aim is to both qualitatively and quantitatively assess the cost of implementing these protocols, which is a topic that has ignited significant interest recently [5,[8][9][10][11][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38]. Indeed as discussed in [2] the notion of the cost has been somewhat loosely employed and therefore different quantifiers probe different aspects of the systemʼs energy or its interactions.…”

“…The question of how to quantify the necessary resources to control a quantum system using a particular protocol has recently become a topic of intense research activity (indeed, in the context of thermodynamic cycles the issue becomes more subtle since any additional energy which is not dissipated can in principle be recycled and act as a catalyst [20]). The variety of ways in which a particular set-up can be coherently controlled has led to a plethora of definitions [5,[8][9][10][11][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38]. Nevertheless, since many of these quantifiers invariably share some common traits, it leads to a natural question: which control protocols are the most resource intensive?…”

Optimizing NMR quantum information processing via generalized transitionless quantum driving

“…In general, H 0 (t) is identified as a slowly piecewise time-dependent Hamiltonian, so that the adiabatic dynamics can be achieved. The parameters θ n (t) are real arbitrary func-arXiv:1906.08065v1 [quant-ph] 19 Jun 2019 tions to be adjusted in order to optimize some physical relevant quantity [29] or, as we shall see, optimize some pulse sequence for achieving some output state in NMR quantum information processing. Thus, from a general definition of U(t), the driving generalized transitionless Hamiltonian reads [29] H gen…”

An efficient nonlinear Feshbach engine

“…While these approaches have often centered around non-interacting systems, STAs have also been explored in interacting, nonlinear, and other systems [20][21][22][23][24][25]. Remarkably, STAs have fundamental implications on quantum speed limits (QSL) [26][27][28][29][30], time-energy uncertainty relations (or energy cost) [31][32][33][34][35][36][37][38], and the quantification of the third law of thermodynamics in the context of quantum refrigerators [39,40], which results in intriguing practical applications in heat engines [41][42][43][44][45][46][47].…”