Nonadiabatic quantum state engineering driven by fast quench dynamics

Abstract

There are a number of tasks in quantum information science that exploit non-transitional adiabatic dynamics. Such a dynamics is bounded by the adiabatic theorem, which naturally imposes a speed limit in the evolution of quantum systems. Here, we investigate an approach for quantum state engineering exploiting a shortcut to the adiabatic evolution, which is based on rapid quenches in a continuous-time Hamiltonian evolution. In particular, this procedure is able to provide state preparation faster than the adiabatic brachistochrone. Remarkably, the evolution time in this approach is shown to be ultimately limited by its "thermodynamical cost," provided in terms of the average work rate (average power) of the quench process. We illustrate this result in a scenario that can be experimentally implemented in a nuclear magnetic resonance setup.

Shortcuts to adiabaticity: Concepts, methods, and applications

“…Such a hybrid strategy has been explicitly worked out to engineer spin like systems (Hegerfeldt, 2013;Sun et al, 2017;Zhou et al, 2017a), to minimize final excitation after a fast transport in the presence of anharmonicities , to ensure fast transport with extra relevant constraints (e.g. minimum transient energy, bounded trap velocity, or bounded distance from the trap center) Amri et al, 2018;Chen et al, 2011b;Stefanatos and Li, 2014;, to ensure a fast and robust shuttling of an ion with noise (Lu et al, 2014d), to perform fast expansions (Boldt et al, 2016;Lu et al, 2014c;Plata et al, 2019;Salamon et al, 2009;Stefanatos, 2013Stefanatos, , 2017bStefanatos et al, 2010), or to drive a many-body Lipkin-Meshkov-Glick system (Campbell et al, 2015).…”

Energetic cost of quantum control protocols

“…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?…”

Quantum adiabatic brachistochrone for open systems

“…This quantum formulation of a variational principle to find the optimal dynamics has been used in different contexts [3][4][5], such as quantum computation [6][7][8] and optimal control [9]. It is particularly promising in the field of quantum computation, where the notion of quantum adiabatic brachistochrone (QAB) for unitary dynamics has been introduced one decade ago by Rezakhani et al [10]: It allows one to implement efficiently quantum algorithms and quantum tasks using an adiabatic dynamics [11,12].…”