We discuss the energetic cost of superadiabatic models of quantum computation. Specifically, we investigate the energy-time complementarity in general transitionless controlled evolutions and in shortcuts to the adiabatic quantum search over an unstructured list. We show that the additional energy resources required by superadiabaticity for arbitrary controlled evolutions can be minimized by using probabilistic dynamics, so that the optimal success probability is fixed by the choice of the evolution time. In the case of analog quantum search, we show that the superadiabatic approach induces a non-oracular counter-diabatic Hamiltonian, with the same energy-time complexity as equivalent adiabatic implementations.
We discuss the energetic cost of superadiabatic models of quantum computation. Specifically, we investigate the energy-time complementarity in general transitionless controlled evolutions and in shortcuts to the adiabatic quantum search over an unstructured list. We show that the additional energy resources required by superadiabaticity for arbitrary controlled evolutions can be minimized by using probabilistic dynamics, so that the optimal success probability is fixed by the choice of the evolution time. In the case of analog quantum search, we show that the superadiabatic approach induces a non-oracular counter-diabatic Hamiltonian, with the same energy-time complexity as equivalent adiabatic implementations.
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.
\n\nAdiabatic and superadiabatic controlled evolutions are used as universal models for quantum computations, where an auxiliary system is used as the main resource in the theory. While the adiabatic case demands a slow dynamics (so that the adiabatic theorem is satisfied), the superadiabatic model can speed up such process by spending more energy than the adiabatic one. In this paper, we explore a hybrid scheme of controlled evolutions and measurement in order to optimize the thermodynamic cost of implementing quantum gates. By adjusting a free parameter of the theory of controlled evolutions, we show that we can improve the energy cost of the evolution. To this end, we used a model of computation based on adiabatic/superadiabatic evolution and post-selection measurement on the auxiliary qubit. In both cases, adiabatic and superadiabatic, the probabilistic model allows for optimizing the thermodynamics cost of implementing gates. When the system reservoir interaction is taken into account, we show that the superadiabatic probabilistic model is more robust than the adiabatic one.\n
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.
We introduce a shortcut to the adiabatic gate teleportation model of quantum computation. More specifically, we determine fast local counterdiabatic Hamiltonians able to implement teleportation as a universal computational primitive. In this scenario, we provide the counterdiabatic driving for arbitrary n-qubit gates, which allows to achieve universality through a variety of gate sets. Remarkably, our approach maps the superadiabatic Hamiltonian HSA for an arbitrary n-qubit gate teleportation into the implementation of a rotated superadiabatic dynamics of an n-qubit state teleportation. This result is rather general, with the speed of the evolution only dictated by the quantum speed limit. In particular, we analyze the energetic cost for different Hamiltonian interpolations in the context of the energy-time complementarity.
Adiabatic time-optimal quantum controls are extensively used in quantum technologies to break the constraints imposed by short coherence times. However, practically it is crucial to consider the trade-off between the quantum evolution speed and instantaneous energy cost of process because of the constraints in the available control Hamiltonian. Here, we experimentally show that using a transmon qubit that, even in the presence of vanishing energy gaps, it is possible to reach a highly time-optimal adiabatic quantum driving at low energy cost in the whole evolution process. This validates the recently derived general solution of the quantum Zermelo navigation problem, paving the way for energy-efficient quantum control which is usually overlooked in conventional speed-up schemes, including the well-known counter-diabatic driving. By designing the control Hamiltonian based on the quantum speed limit bound quantified by the changing rate of phase in the interaction picture, we reveal the relationship between the quantum speed limit and instantaneous energy cost. Consequently, we demonstrate fast and high-fidelity quantum adiabatic processes by employing energy-efficient driving strengths, indicating a promising strategy for expanding the applications of time-optimal quantum controls in superconducting quantum circuits.
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.