Adiabatic Shortcuts Completion in Quantum Field Theory: Annihilation of Created Particles.

Shortcuts to adiabaticity (STA) are relevant in the context of quantum systems, particularly regarding their control when they are subjected to time-dependent external conditions. In this paper, we investigate the completion of a nonadiabatic evolution into a shortcut to adiabaticity for a quantum field confined within a one-dimensional cavity containing two movable mirrors. Expanding upon our prior research, we characterize the field's state using two Moore functions that enables us to apply reverse engineering techniques in constructing the STA. Regardless of the initial evolution, we achieve a smooth extension of the Moore functions that implements the STA. This extension facilitates the computation of the mirrors' trajectories based on the aforementioned functions. Additionally, we draw attention to the existence of a comparable problem within nonrelativistic quantum mechanics.

Optimal Shortcuts to Adiabatic Control by Lagrange Mechanics.

We combined an inverse engineering technique based on Lagrange mechanics and optimal control theory to design an optimal trajectory that can transport a cartpole in a fast and stable way. For classical control, we used the relative displacement between the ball and the trolley as the controller to study the anharmonic effect of the cartpole. Under this constraint, we used the time minimization principle in optimal control theory to find the optimal trajectory, and the solution of time minimization is the bang-bang form, which ensures that the pendulum is in a vertical upward position at the initial and the final moments and oscillates in a small angle range.

Fast ion shuttling which is robust versus oscillatory perturbations.

Shuttling protocols designed by shortcut-to-adiabaticity techniques may suffer from perturbations and imperfect implementations. We study the motional excitation of a single ion shuttled in harmonic traps with time-dependent, 'systematic' oscillatory perturbations around the nominal parameters. These elementary perturbations could form any other by superposition. Robust shuttling strategies are proposed and compared, and optimizations are performed. This article is part of the theme issue 'Shortcuts to adiabaticity: theoretical, experimental and interdisciplinary perspectives'.

Optimal shortcuts of stimulated Raman adiabatic passage in the presence of dissipation.

We use optimal control theory to obtain shortcuts to adiabaticity which maximize population transfer in a three-level stimulated Raman adiabatic passage system, for a given finite duration of the process and a specified dissipation rate at the intermediate state. We fix the sum of the intensities of the pump and Stokes pulses and use the mixing angle of the fields as the sole control variable. We determine the optimal variation of this angle and reveal the role of the singular arc in the optimal trajectory, in order to minimize the effect of dissipation. This article is part of the theme issue 'Shortcuts to adiabaticity: theoretical, experimental and interdisciplinary perspectives'.

Fast-forward scaling theory.

Speed is the key to further advances in technology. For example, quantum technologies, such as quantum computing, require fast manipulations of quantum systems in order to overcome the effect of decoherence. However, controlling the speed of quantum dynamics is often very difficult due to both the lack of a simple scaling property in the dynamics and the infinitely large parameter space to be explored. Therefore, protocols for speed control based on understanding of the dynamical properties of the system, such as non-trivial scaling property, are highly desirable. Fast-forward scaling theory (FFST) was originally developed to provide a way to accelerate, decelerate, stop and reverse the dynamics of quantum systems. FFST has been extended in order to accelerate quantum and classical adiabatic dynamics of various systems including cold atoms, internal state of molecules, spins and solid-state artificial atoms. This paper describes the basic concept of FFST and reviews the recent developments and its applications such as fast state-preparations, state protection and ion sorting. We introduce a method, called inter-trajectory travel, recently derived from FFST. We also point out the significance of deceleration in quantum technology. This article is part of the theme issue 'Shortcuts to adiabaticity: theoretical, experimental and interdisciplinary perspectives'.

Robust electron spin qubit control in a nanowire double quantum dot.

Robust and efficient manipulation of electron spin qubits in quantum dots is of great significance for the reliable realization of quantum computers and execution of quantum algorithms. In this paper, we study the robust control on a singlet-triplet qubit based on inverse engineering, one technique of shortcuts to adiabaticity (STA), in a nanowire double quantum dot in the presence of magnetic field and strong spin-orbit coupling. The optimization of STA with respect to the systematic errors, contributed from the control field and the perturbative interaction, is explored. Moreover, we also apply optimal control techniques combining with STA, referred to as robust inverse optimization, to design optimal control fields and optimal operation time. This article is part of the theme issue 'Shortcuts to adiabaticity: theoretical, experimental and interdisciplinary perspectives'.

Fast transport of Bose-Einstein condensates in anharmonic traps.

We present a method to transport Bose-Einstein condensates (BECs) in anharmonic traps and in the presence of atom-atom interactions in short times without residual excitation. Using a combination of a variational approach and inverse engineering methods, we derive a set of Ermakov-like equations that take into account the coupling between the centre of mass motion and the breathing mode. By an appropriate inverse engineering strategy of those equations, we then design the trap trajectory to achieve the desired boundary conditions. Numerical examples for cubic or quartic anharmonicities are provided for fast and high-fidelity transport of BECs. Potential applications are atom interferometry and quantum information processing. This article is part of the theme issue 'Shortcuts to adiabaticity: theoretical, experimental and interdisciplinary perspectives'.

Tailored ion beam for precise colour centre creation.

We present an invariant-based quantum control scheme leading to a highly monochromatic ion beam from a Paul trap. Our protocol is implementable by supplying the segmented electrodes in the trap with voltages of the order of volts. This mitigates the impact of fluctuations in previous designs and leads to a low-dispersion beam of ions. Moreover, our proposal does not rely on sympathetically cooling ions, which bypasses the need of loading different species in the trap-namely, the propelled ion and, e.g. a [Formula: see text] to exert sympathetic cooling-significantly incrementing the repetition rate of the launching procedure. Our scheme is based on an invariant operator linear in position and momentum, which enables us to control the average extraction energy and the outgoing momentum spread. In addition, we propose a sequential operation to tailor the transversal properties of the beam before the ejection to minimize the impact spot and to increase the lateral resolution of the implantation. This article is part of the theme issue 'Shortcuts to adiabaticity: theoretical, experimental and interdisciplinary perspectives'.

Fast Driving of a Particle in Two Dimensions without Final Excitation.

Controlling the motional state of a particle in a multidimensional space is key for fundamental science and quantum technologies. Applying a recently found two-dimensional invariant combined with linear invariants, we propose protocols to drive a particle in two dimensions so that the final harmonic trap is translated and rotated with respect to the initial one. These protocols realize a one-to-one mapping between initial and final eigenstates at some predetermined time and avoid any final excitations.

Fast Adiabatic Control of an Optomechanical Cavity.

The development of quantum technologies present important challenges such as the need for fast and precise protocols for implementing quantum operations. Shortcuts to adiabaticity (STAs) are a powerful tool for achieving these goals, as they enable us to perform an exactly adiabatic evolution in finite time. In this paper, we present a shortcut to adiabaticity for the control of an optomechanical cavity with two moving mirrors. Given reference trajectories for the mirrors, we find analytical expressions that give us effective trajectories which implement an STA for the quantum field inside the cavity. We then solve these equations numerically for different reference protocols, such as expansions, contractions and rigid motions, thus confirming the successful implementation of the STA and finding some general features of these effective trajectories.

Environment-Assisted Shortcuts to Adiabaticity.

Envariance is a symmetry exhibited by correlated quantum systems. Inspired by this "quantum fact of life," we propose a novel method for shortcuts to adiabaticity, which enables the system to evolve through the adiabatic manifold at all times, solely by controlling the environment. As the main results, we construct the unique form of the driving on the environment that enables such dynamics, for a family of composite states of arbitrary dimension. We compare the cost of this environment-assisted technique with that of counterdiabatic driving, and we illustrate our results for a two-qubit model.

Connection between Inverse Engineering and Optimal Control in Shortcuts to Adiabaticity.

We consider fast high-fidelity quantum control by using a shortcut to adiabaticity (STA) technique and optimal control theory (OCT). Three specific examples, including expansion of cold atoms from the harmonic trap, atomic transport by moving harmonic trap, and spin dynamics in the presence of dissipation, are explicitly detailed. Using OCT as a qualitative guide, we demonstrate how STA protocols designed from inverse engineering method can approach with very high precision optimal solutions built about physical constraints, by a proper choice of the interpolation function and with a very reduced number of adjustable parameters.

Time-Rescaling of Dirac Dynamics: Shortcuts to Adiabaticity in Ion Traps and Weyl Semimetals.

Only very recently, rescaling time has been recognized as a way to achieve adiabatic dynamics in fast processes. The advantage of time-rescaling over other shortcuts to adiabaticity is that it does not depend on the eigenspectrum and eigenstates of the Hamiltonian. However, time-rescaling requires that the original dynamics are adiabatic, and in the rescaled time frame, the Hamiltonian exhibits non-trivial time-dependence. In this work, we show how time-rescaling can be applied to Dirac dynamics, and we show that all time-dependence can be absorbed into the effective potentials through a judiciously chosen unitary transformation. This is demonstrated for two experimentally relevant scenarios, namely for ion traps and adiabatic creation of Weyl points.

Noise Sensitivities for an Atom Shuttled by a Moving Optical Lattice via Shortcuts to Adiabaticity.

We find the noise sensitivities (i.e., the quadratic terms of the energy with respect to the perturbation of the noise) of a particle shuttled by an optical lattice that moves according to a shortcut-to-adiabaticity transport protocol. Noises affecting different optical lattice parameters, trap depth, position, and lattice periodicity, are considered. We find generic expressions of the sensitivities for arbitrary noise spectra but focus on the white-noise limit as a basic reference, and on Ornstein-Uhlenbeck noise to account for the effect of non-zero correlation times.

Invariant-Based Inverse Engineering for Fast and Robust Load Transport in a Double Pendulum Bridge Crane.

We set a shortcut-to-adiabaticity strategy to design the trolley motion in a double-pendulum bridge crane. The trajectories found guarantee payload transport without residual excitation regardless of the initial conditions within the small oscillations regime. The results are compared with exact dynamics to set the working domain of the approach. The method is free from instabilities due to boundary effects or to resonances with the two natural frequencies.

Nonadiabatic Energy Fluctuations of Scale-Invariant Quantum Systems in a Time-Dependent Trap.

We consider the nonadiabatic energy fluctuations of a many-body system in a time-dependent harmonic trap. In the presence of scale-invariance, the dynamics becomes self-similar and the nondiabatic energy fluctuations can be found in terms of the initial expectation values of the second moments of the Hamiltonian, square position, and squeezing operators. Nonadiabatic features are expressed in terms of the scaling factor governing the size of the atomic cloud, which can be extracted from time-of-flight images. We apply this exact relation to a number of examples: the single-particle harmonic oscillator, the one-dimensional Calogero-Sutherland model, describing bosons with inverse-square interactions that includes the non-interacting Bose gas and the Tonks-Girdardeau gas as limiting cases, and the unitary Fermi gas. We illustrate these results for various expansion protocols involving sudden quenches of the trap frequency, linear ramps and shortcuts to adiabaticity. Our results pave the way to the experimental study of nonadiabatic energy fluctuations in driven quantum fluids.

Shortcuts to Adiabaticity for Optical Beam Propagation in Nonlinear Gradient Refractive-Index Media.

In recent years, the concept of "shortcuts to adiabaticity" has been originally proposed to speed up sufficiently slow adiabatic process in various quantum systems without final excitation. Based on the analogy between classical optics and quantum mechanics, we present a study on fast non-adiabatic compression of optical beam propagation in nonlinear gradient refractive-index media by using shortcuts to adiabaticity. We first apply the variational approximation method in nonlinear optics to derive the auxiliary equation for connecting the beam width with the refractive index of the medium. Then, the gradient refractive index is inversely designed through the perfect compression of beam width with the appropriate boundary conditions. Finally, the comparison with conventional adiabatic compression is made, showing the advantage of our shortcuts.

Digital Quantum Simulation of Nonadiabatic Geometric Gates via Shortcuts to Adiabaticity.

Geometric phases are used to construct quantum gates since it naturally resists local noises, acting as the modularized units of geometric quantum computing. Meanwhile, fast nonadiabatic geometric gates are required for reducing the information loss induced by decoherence. Here, we propose a digital simulation of nonadiabatic geometric quantum gates in terms of shortcuts to adiabaticity (STA). More specifically, we combine the invariant-based inverse engineering with optimal control theory for designing the fast and robust Abelian geometric gates against systematic error, in the context of two-level qubit systems. We exemplify X and T gates, in which the fidelities and robustness are evaluated by simulations in ideal quantum circuits. Our results can also be extended to constructing two-qubit gates, for example, a controlled-PHASE gate, which shares the equivalent effective Hamiltonian with rotation around the Z-axis of a single qubit. These STA-inspired nonadiabatic geometric gates can realize quantum error correction physically, leading to fault-tolerant quantum computing in the Noisy Intermediate-Scale Quantum (NISQ) era.

Shortcut-to-Adiabaticity-Like Techniques for Parameter Estimation in Quantum Metrology.

Quantum metrology makes use of quantum mechanics to improve precision measurements and measurement sensitivities. It is usually formulated for time-independent Hamiltonians, but time-dependent Hamiltonians may offer advantages, such as a T4 time dependence of the Fisher information which cannot be reached with a time-independent Hamiltonian. In Optimal adaptive control for quantum metrology with time-dependent Hamiltonians (Nature Communications 8, 2017), Shengshi Pang and Andrew N. Jordan put forward a Shortcut-to-adiabaticity (STA)-like method, specifically an approach formally similar to the "counterdiabatic approach", adding a control term to the original Hamiltonian to reach the upper bound of the Fisher information. We revisit this work from the point of view of STA to set the relations and differences between STA-like methods in metrology and ordinary STA. This analysis paves the way for the application of other STA-like techniques in parameter estimation. In particular we explore the use of physical unitary transformations to propose alternative time-dependent Hamiltonians which may be easier to implement in the laboratory.

Approaching the adiabatic timescale with machine learning.

The control and manipulation of quantum systems without excitation are challenging, due to the complexities in fully modeling such systems accurately and the difficulties in controlling these inherently fragile systems experimentally. For example, while protocols to decompress Bose-Einstein condensates (BECs) faster than the adiabatic timescale (without excitation or loss) have been well developed theoretically, experimental implementations of these protocols have yet to reach speeds faster than the adiabatic timescale. In this work, we experimentally demonstrate an alternative approach based on a machine-learning algorithm which makes progress toward this goal. The algorithm is given control of the coupled decompression and transport of a metastable helium condensate, with its performance determined after each experimental iteration by measuring the excitations of the resultant BEC. After each iteration the algorithm adjusts its internal model of the system to create an improved control output for the next iteration. Given sufficient control over the decompression, the algorithm converges to a solution that sets the current speed record in relation to the adiabatic timescale, beating out other experimental realizations based on theoretical approaches. This method presents a feasible approach for implementing fast-state preparations or transformations in other quantum systems, without requiring a solution to a theoretical model of the system. Implications for fundamental physics and cooling are discussed.