There are a number of tasks in quantum information science that exploit nontransitional 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.
There are a number of tasks in quantum information science that exploit nontransitional 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.
Adiabatic state engineering is a powerful technique in quantum information and quantum control. However, its performance is limited by the adiabatic theorem of quantum mechanics. In this scenario, shortcuts to adiabaticity, such as provided by the superadiabatic theory, constitute a valuable tool to speed up the adiabatic quantum behavior. Here, we propose a superadiabatic route to implement universal quantum computation. Our method is based on the realization of piecewise controlled superadiabatic evolutions. Remarkably, they can be obtained by simple time-independent counter-diabatic Hamiltonians. In particular, we discuss the implementation of fast rotation gates and arbitrary n-qubit controlled gates, which can be used to design different sets of universal quantum gates. Concerning the energy cost of the superadiabatic implementation, we show that it is dictated by the quantum speed limit, providing an upper bound for the corresponding adiabatic counterparts.
Adiabatic evolution is a powerful technique in quantum information and computation. However, its performance is limited by the adiabatic theorem of quantum mechanics. In this scenario, shortcuts to adiabaticity, such as provided by the superadiabatic theory, constitute a valuable tool to speed up the adiabatic quantum behavior. In this dissertation we introduce two different models to perform universal superadiabatic quantum computing, which are based on the use of shortcuts to adiabaticity by counter-diabatic Hamiltonians. The first model is based on the use of superadiabatic quantum teleportation, introduced in this dissertation, as a primitive to quantum computing. Thus, we provide the counter-diabatic driving for arbitrary n-qubit gates. In addition, our approach maps the counter-diabatic Hamiltonian for an arbitrary n-qubit {\it gate} teleportation into the implementation of a rotated counter-diabatic Hamiltonian for an n-qubit {\it state} teleportation. In the second model we use the concept of controlled superadiabatic evolutions to show how we can implement arbitrary n-controlled quantum gates. Remarkably, this task can be performed by simple time-independent counter-diabatic Hamiltonians. These two models can be used to design different sets of universal quantum gates. We show that the use of the quantum speed limit suggests that the superadiabatic time evolution is compatible with arbitrarily small time intervals, where this arbitrariness is constrained to the energetic cost necessary to perform the superadiabatic evolution.
Abstract Shortcuts to adiabaticity provide a general approach to mimic adiabatic quantum processes via arbitrarily fast evolutions in Hilbert space. For these counter-diabatic evolutions, higher speed comes at higher energy cost. Here, the counter-diabatic 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.
Quantum adiabatic processes—that keep constant the populations in the instantaneous eigenbasis of a time-dependent Hamiltonian—are very useful to prepare and manipulate states, but take typically a long time. This is often problematic because decoherence and noise may spoil the desired final state, or because some applications require many repetitions. "Shortcuts to adiabaticity" are alternative fast processes which reproduce the same final populations, or even the same final state, as the adiabatic process in a finite, shorter time. Since adiabatic processes are ubiquitous, the shortcuts span a broad range of applications in atomic, molecular, and optical physics, such as fast transport of ions or neutral atoms, internal population control, and state preparation (for nuclear magnetic resonance or quantum information), cold atom expansions and other manipulations, cooling cycles, wavepacket splitting, and many-body state engineering or correlations microscopy. Shortcuts are also relevant to clarify fundamental questions such as a precise quantification of the third principle of thermodynamics and quantum speed limits. We review different theoretical techniques proposed to engineer the shortcuts, the experimental results, and the prospects.
The ability to efficiently prepare ground states of quantum Hamiltonians via adiabatic protocols is typically limited by the smallest energy gap encountered during the quantum evolution. This presents a key obstacle for quantum simulation and realizations of adiabatic quantum algorithms in large systems, particularly when the adiabatic gap vanishes exponentially with system size. Using QuEra's Aquila programmable quantum simulator based on Rydberg atom arrays, we experimentally demonstrate a method to circumvent such limitations. Specifically, we develop and test a "sweep-quench-sweep" quantum algorithm in which the incorporation of a quench step serves as a remedy to the diverging adiabatic timescale. These quenches introduce a macroscopic reconfiguration between states separated by an extensively large Hamming distance, akin to quantum many-body scars. Our experiments show that this approach significantly outperforms the adiabatic algorithm, illustrating that such quantum quench algorithms can provide a shortcut to adiabaticity for large-scale many-body quantum systems.
The quantum adiabatic method, which maintains populations in their instantaneous eigenstates throughout the state evolution, is an established and often a preferred choice for state preparation and manipulation. Although it minimizes the driving cost significantly, its slow speed is a severe limitation in noisy intermediate-scale quantum era technologies. Since adiabatic paths are extensive in many physical processes, it is of broader interest to achieve adiabaticity at a much faster rate. Shortcuts to adiabaticity techniques, which overcome the slow adiabatic process by driving the system faster through non-adiabatic paths, have seen increased attention recently. The extraordinarily long lifetime of the long-lived singlet states (LLS) in nuclear magnetic resonance (NMR), established over the past decade, has opened several important applications ranging from spectroscopy to biomedical imaging. Various methods, including adiabatic methods, are already being used to prepare LLS. In this article, we report the use of counterdiabatic driving (CD) to speed up LLS preparation with faster drives. Using NMR experiments, we show that CD can give stronger LLS order in shorter durations than conventional adiabatic driving.