Fast and robust quantum gates is the cornerstone of fault-tolerance quantum computation. In this paper, we propose to achieve quantum gates based on non-cyclic geometric evolution. Dynamical phase during the evolution is cancelled by spin-echo process and the adiabatic control can be sped up through shortcut to adiabatic manner. Different from geometric gates based on cyclic evolution, the superiority of non-cyclic scheme is that the operation time is proportional to the rotation angle (but not the geometric phase) of quantum state. Therefore, the non-cyclic scheme becomes fairly fast in the case of quantum gates with small rotation angle which will be more insensitive to the decoherence and leakage to the states outside the computational basis. The proposed scheme is also robust against random noise due to the geometric characteristic of projective Hilbert space. Since the refined proposed scheme is fast and robust, it is an particularly suitable way to manipulate the physical systems with weak nonlinearity, such as superconucting systems.
Pedagogical introduction to counterdiabatic formalism of shortcuts to adiabaticity is given so that the readers are accessible to some of more specialized articles in the rest of this theme issue without a much barrier. A guide to references is given so that this article also serves as a mini-review.
Different techniques to speed up quantum adiabatic processes are currently being explored for applications in atomic, molecular and optical physics, such as transport, cooling and expansions, wavepacket splitting, or internal state control. Here we examine the capabilities of superadiabatic iterations to produce a sequence of shortcuts to adiabaticity. The general formalism is worked out as well as examples for population inversion in a two-level system.
Shortcuts to adiabaticity are alternative fast processes that reproduce the same final populations, or even the same final state, as the adiabatic process in a finite, shorter time. Many of the existing approaches to design shortcuts, and even new ones have been used throughout this Thesis in the double well potential. These techniques have allowed us to obtain a great benefit in processes as varied as matter-wave splitting, multiplexing/ demultiplexing, beam splitters, cotunneling, population inversion, waveguide optimization, Tonks-Girardeau gas manipulation and bias inversion.
A non-Hermitian shortcut to adiabaticity is introduced. By adding an imaginary term in the diagonal elements of the Hamiltonian of a two state quantum system, we show how one can cancel the nonadiabatic losses and perform an arbitrarily fast population transfer, without the need to increase the coupling. We apply this technique to two popular level-crossing models: the Landau-Zener model and the Allen-Eberly model.
In fast forward quantum shortcuts to adiabaticity, a designed potential $U_{FF}(q,t)$ steers a wavefunction to evolve from the $n$'th eigenstate of an initial Hamiltonian $\hat H(0)$ to the $n$'th eigenstate of a final Hamiltonian $\hat H(τ)$, in finite time $τ$. Previously proposed strategies for constructing $U_{FF}$ are (in the absence of special symmetries) limited to the ground state, $n=0$. We develop a method that overcomes this limitation, thereby substantially expanding the applicability of this shortcut to adiabaticity, and we illustrate its effectiveness with numerical simulations. …
We discuss applications of shortcuts to adiabaticity (STA) to adiabatic quantum computation. After reviewing the fundamental properties and the present status of STA from the author's personal point of view, we apply the method to the adiabatic algorithm of the Grover's problem. We discuss two possible implementations of STA for the adiabatic quantum computations: the method of quantum adiabatic brachistochrone and the Lewis-Riesenfeld invariant-based inverse engineering.
Shortcuts to adiabaticity (STA) are fast routes to the final results of slow, adiabatic changes of the controlling parameters of a system. The shortcuts are designed by a set of analytical and numerical methods suitable for different systems and conditions. A motivation to apply STA methods to quantum systems is to manipulate them on timescales shorter than decoherence times. Thus shortcuts to adiabaticity have become instrumental in preparing and driving internal and motional states in atomic, molecular, and solid-state physics. Applications range from information transfer and processing base…
We give a pedagogical introduction to dynamical invariant formalism of shortcuts to adiabaticity. For a given operator form of the Hamiltonian with undetermined coefficients, the dynamical invariant is introduced to design the coefficients. We discuss how the method allows us to realize adiabatic dynamics and describe a relation to the counterdiabatic formalism. The equation for the dynamical invariant takes a familiar form and is often used in various fields of physics. We introduce examples of Lax pair, quantum brachistochrone, and flow equation.
We study the Ising Hamiltonian with a transverse field term to simulate the quantum annealing. Using shortcuts to adiabaticity, we design the time dependence of the Hamiltonian. The dynamical invariant is obtained by the mean-field ansatz, and the Hamiltonian is designed by the inverse engineering. We show that the time dependence of physical quantities such as the magnetization is independent of the speed of the Hamiltonian variation in the infinite-range model. We also show that rotating transverse magnetic fields are useful to achieve the ideal time evolution.
Sped-up protocols (shortcuts to adiabaticity) that drive a system quickly to the same populations than a slow adiabatic process may involve Hamiltonian terms difficult to realize in practice. We use the dynamical symmetry of the Hamiltonian to find, by means of Lie transforms, alternative Hamiltonians that achieve the same goals without the problematic terms. We apply this technique to three-level systems (two interacting bosons in a double well, and beam splitters with two and three output channels) driven by Hamiltonians that belong to the four-dimensional algebra U3S3.
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 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.
Shortcuts to adiabaticity let a system reach the results of a slow adiabatic process in a shorter time. We propose to quantify the "energy cost" of the shortcut by the energy consumption of the system enlarged by including the control device. A mechanical model where the dynamics of the system and control device can be explicitly described illustrates that a broad range of possible values for the consumption are possible, including zero (above the adiabatic energy increment) when friction is negligible and the energy given away as negative power is stored and recovered by perfect regenerative …
A combination of the digitized shortcut-to-adiabaticity (STA) and the sequential digitized adiabaticity is implemented in a superconducting quantum device to determine electronic states in two example systems, the H2 molecule and the topological Bernevig-Hughes-Zhang (BHZ) model. For H2, a short internuclear distance is chosen as a starting point, at which the ground and excited states are obtained via the digitized STA. From this starting point, a sequence of internuclear distances is built. The eigenstates at each distance are sequentially determined from those at the previous distance via t…
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 red…
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.
The quantum perceptron is a fundamental building block for quantum machine learning. This is a multidisciplinary field that incorporates abilities of quantum computing, such as state superposition and entanglement, to classical machine learning schemes. Motivated by the techniques of shortcuts to adiabaticity, we propose a speed-up quantum perceptron where a control field on the perceptron is inversely engineered leading to a rapid nonlinear response with a sigmoid activation function. This results in faster overall perceptron performance compared to quasi-adiabatic protocols, as well as in en…
A Schrödinger equation may be transformed by unitary operators into dynamical equations in different interaction pictures which share with it a common physical frame, i.e., the same underlying interactions, processes and dynamics. In contrast to this standard scenario, other relations are also possible, such as a common interaction-picture dynamical equation corresponding to several Schrödinger equations that represent different physics. This may enable us to design alternative and feasible experimental routes for operations that are a priori difficult or impossible to perform. The power of th…
Achieving effectively adiabatic dynamics in finite time is a ubiquitous goal in virtually all areas of modern physics. So-called shortcuts to adiabaticity refer to a set of methods and techniques that allow to produce in a short time the same final state that would result from an adiabatic, infinitely slow process. In the present work we generalize one of these methods -- the fast-forward technique -- to driven Dirac dynamics. As a main result we find that shortcuts to adiababticity for the $(1+1)$-dimensional Dirac equation are facilitated by a combination of both, scalar and pseudoscalar pot…
We propose how to engineer the longitudinal coupling to accelerate the measurement of a qubit longitudinally coupled to a cavity, motivated by the concept of shortcuts to adiabaticity. Different modulations are inversely designed from two methods of inverse engineering and counter-diabatic driving, for achieving larger values of the signal-to-noise ratio (SNR) at nanosecond scale. By comparison, we demonstrate that our protocols outperform the usual periodic modulations on the pointer state separation and SNR. Finally, we show a possible implementation considering state-of-the-art circuit quan…
We show that the quantum Fisher information attained in an adiabatic approach to critical quantum metrology cannot lead to the Heisenberg limit of precision and therefore regular quantum metrology under optimal settings is always superior. Furthermore, we argue that even though shortcuts to adiabaticity can arbitrarily decrease the time of preparing critical ground states, they cannot be used to achieve or overcome the Heisenberg limit for quantum parameter estimation in adiabatic critical quantum metrology. As case studies, we explore the application of counter-diabatic driving to the Landau-…
The design of quantum control methods has been shown to greatly improve the performance of many evolving quantum technologies. To this end, the usage of adiabatic dynamics to drive quantum systems is seriously limited by the action of environment-induced noise and decoherence. In this spirit, fast quantum processes known as shortcuts to adiabaticity have been developed as alternatives to adiabatic protocols with a myriad of potential applications. Here, we develop a new state-independent mechanism to speed up the evolution of an arbitrary quantum dynamical system by simply rescaling the time o…
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 s…
Adiabatic processes driven by non-Hermitian, time-dependent Hamiltonians may be sped up by generalizing inverse engineering techniques based on Berry's transitionless driving algorithm or on dynamical invariants. We work out the basic theory and examples described by two-level Hamiltonians: the acceleration of rapid adiabatic passage with a decaying excited level and of the dynamics of a classical particle on an expanding harmonic oscillator.
We engineer the fast rotation of a quantum particle confined in an effectively one-dimensional, harmonic trap, for a predetermined rotation angle and time, avoiding final excitation. Different schemes are proposed with different speed limits that depend on the control capabilities. We also make use of trap rotations to create squeezed states without manipulating the trap frequencies.
Using shortcuts to adiabaticity, we solve the time-dependent Schroedinger equation that is reduced to a classical nonlinear integrable equation. For a given time-dependent Hamiltonian, the counterdiabatic term is introduced to prevent nonadiabatic transitions. Using the fact that the equation for the dynamical invariant is equivalent to the Lax equation in nonlinear integrable systems, we obtain the counterdiabatic term exactly. The counterdiabatic term is available when the corresponding Lax pair exists and the solvable systems are classified in a unified and systematic way. Multisoliton pote…
Achieving effectively adiabatic dynamics is a ubiquitous goal in almost all areas of quantum physics. Here, we study the speed with which a quantum system can be driven when employing transitionless quantum driving. As a main result, we establish a rigorous link between this speed, the quantum speed limit, and the (energetic) cost of implementing such a shortcut to adiabaticity. Interestingly, this link elucidates a trade-off between speed and cost, namely that instantaneous manipulation is impossible as it requires an infinite cost. These findings are illustrated for two experimentally releva…
NOON states play the important roles in quantum information processings and quantum metrology, but the fidelities of these states generated previously are limited typically by the practically-unavoidable decoherence and operational imperfections. Here, we propose an efficient scheme to generate photonic NOON states alternatively by rapid population passage technique via shortcut to adiabaticity (STA), rather than the usual Rabi oscillations. Since the deterministic population passages based on the STAs are insensitive to details of the operations and can be implemented as fast as the Rabi osci…
Shortcut to adiabaticity (STA) is a speed way to produce the same final state that would result in an adiabatic, infinitely slow process. Two typical techniques to engineer STA are developed by either introducing auxiliary counterdiabatic fields or finding new Hamiltonians that own dynamical invariants to constraint the system into the adiabatic paths. In this paper, a consistent method is introduced to naturally connect the above two techniques with a unified Lie algebraic framework, which neatly removes the requirements of finding instantaneous states in the transitionless driving method and…
We show that the performances of a Stern-Gerlach apparatus can be improved by using a magnetic field profile for the atomic spin evolution designed through shortcut to adiabaticity technique. Interestingly, it can be made more compact - for atomic beams propagating at a given velocity - and more resilient to a dispersion in velocity, in comparison with the results obtained with a standard uniform rotation of the magnetic field. Our results are obtained using a reverse engineering approach based on Lewis-Riesenfeld invariants. We discuss quantitatively the advantages offered by our configuratio…
The "fast-forward" approach by Masuda and Nakamura generates driving potentials to accelerate slow quantum adiabatic dynamics. First we present a streamlined version of the formalism that produces the main results in a few steps. Then we show the connection between this approach and inverse engineering based on Lewis-Riesenfeld invariants. We identify in this manner applications in which the engineered potential does not depend on the initial state. Finally we discuss more general applications exemplified by wave splitting processes.
Suppressing unwanted transitions out of the instantaneous ground state is a major challenge in unitary adiabatic quantum computation. A recent approach consists in building counterdiabatic potentials approximated using variational strategies. In this contribution, we extend this variational approach to Lindbladian dynamics, having as a goal the suppression of diabatic transitions between pairs of Jordan blocks in quantum annealing. We show that, surprisingly, unitary counterdiabatic ansätze are successful for dissipative dynamics as well, allowing for easier experimental implementations compar…
Based on shortcuts to adiabaticity and quantum Zeno dynamics, we present a protocol to implement quantum state transfer (QST) in a quantum spin-1/2 chain. In the protocol, the complex Hamiltonian of an $N$-site system is simplified, and a simple effective Hamiltonian is present. It is shown that only the control of the coupling strengths between the boundary spins and the bulk spins are required for QST. Numerical simulations demonstrate that the protocol possesses high efficiency and is robust against the decay and the fluctuations of the control fields. The protocol might provide an alternat…
Given the increasing use of shotcuts to adiabaticity (STA) to optimize power and efficiency of quantum heat engines, it becomes a relevant question if there are any theoretical limits to their application. We argue that quantum fluctuations in the control device which implements the shortcut deflect the system from the adiabatic path. This not only induces transitions to unwanted final states but also changes the system energy, so that using the STA has a definite cost in terms of conventional work definitions. This may be the ultimate cost of an adiabatic shortcut, in the sense that it is pre…
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 judici…
A highly-efficient method for optical detection and separation of left- and right-handed chiral molecules is presented. The method utilizes a closed-loop three-state system in which the population dynamics depends on the phases of the three couplings. Due to the different signs of the coupling between two of the states for the opposite chiralities and the phase sensitivity of the scheme, the population dynamics is chirality-dependent. By using concepts from the `shortcuts to adiabaticity' approach, one can achieve 100\% contrast in state population transfer between the two enantiomers, which c…
We introduce a bang-bang shortcut to adiabaticity for the Dicke model, which we implement via a 2-D array of trapped ions in a Penning trap with a spin-dependent force detuned close to the center-of-mass drumhead mode. Our focus is on employing this shortcut to create highly entangled states that can be used in high-precision metrology. We highlight that the performance of the bang-bang approach is comparable to standard preparation methods, but can be applied over a much shorter time frame. We compare these theoretical ideas with experimental data which serve as a first step towards realizing…
Fast and robust quantum control protocols are often based on an idealised approximate description of the relevant quantum system. While this may provide a performance which is close to optimal, improvements can be made by incorporating elements of the full system representation. We propose a new technique for such scenarios, called enhanced shortcuts to adiabaticity (eSTA). The eSTA method works for previously intractable Hamiltonians by providing an analytical correction to existing STA protocols. This correction can be easily calculated and the resulting protocols are outside the class of ST…
We propose a fast mixed-state control scheme to transfer the quantum state along designable trajectories in Hilbert space, which is robust to multiple decoherence noises. Starting with the dynamical invariants of open quantum systems, we present the shortcuts to adiabaticity (STAs) of open quantum systems at first, then apply the STAs to speed up the adiabatic steady process. Our scheme drives open systems from a initial steady state to a target steady state by a controlled Liouvillian that possesses the same form as the reference (original) one which is accessible in present-day experiments. …
There is recently a surge of interest to cut down the time it takes to change the state of a quantum system adiabatically. We study for the time-dependent harmonic oscillator the transient energy excitation in speed-up processes designed to reproduce the initial populations at some predetermined final frequency and time, providing lower bounds and examples. Implications for the limits imposed to the process times and for the principle of unattainability of the absolute zero, in a single expansion or in quantum refrigerator cycles, are drawn.
In a `shortcut-to-adiabaticity' (STA) protocol, the counter-diabatic Hamiltonian, which suppresses the non-adiabatic transition of a reference `adiabatic' trajectory, induces a quantum uncertainty of the work cost in the framework of quantum thermodynamics. Following a theory derived recently [Funo et al 2017 Phys. Rev. Lett. 118 100602], we perform an experimental measurement of the STA work statistics in a high-quality superconducting Xmon qubit. Through the frozen-Hamiltonian and frozen-population techniques, we experimentally realize the two-point measurement of the work distribution for g…
Shortcuts to adiabaticity (STA) are fast methods to realize the same final state evolution of quantum adiabatic process. We develop a general theory to construct a new kind of STA by solely sampling the points of the adiabatic path of the original adiabatic Hamiltonian. In contrast to previous methods, our approach does not require any additional control resources, has inherent robustness, and does not use any complicated unitary transformation. Based on path sampling, the resulting STA protocols are simple and can avoid points of adiabatic path that are challenging to implement. As applicatio…
For a frequency-tunable two-qubit system, a controlled-Z (CZ) gate can be realized by adiabatically driving the qubit system through an avoided level crossing between an auxiliary state and computational levels. Here, we theoretically propose a fast CZ gate using a shortcut-to-adiabaticity (STA). Experimentally, the STA CZ gate is implemented with a 52 ns control pulse for two coupled superconducting Xmon qubits. Measured fidelity of the STA CZ gate is higher than 96.0%, in both quantum process tomography and randomized benchmarking. The protocol allows a flexible design of the evolution time …
It is still a challenge to experimentally realize shortcuts to adiabaticity (STA) for a non-Hermitian quantum system since a non-Hermitian quantum system's counterdiabatic driving Hamiltonian contains some unrealizable auxiliary control fields. In this paper, we relax the strict condition in constructing STA and propose a method to redesign a realizable supplementary Hamiltonian to construct non-Hermitian STA. The redesigned supplementary Hamiltonian can be eithersymmetric or asymmetric. For the sake of clearness, we apply this method to an Allen-Eberly model as an example to verify the validi…
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 sp…
Shortcuts to adiabaticity are well-known methods for controlling the quantum dynamics beyond the adiabatic criteria, where counter-diabatic (CD) driving provides a promising means to speed up quantum many-body systems. In this work, we show the applicability of CD driving to enhance the digitized adiabatic quantum computing paradigm in terms of fidelity and total simulation time. We study the state evolution of an Ising spin chain using the digitized version of the standard CD driving and its variants derived from the variational approach. We apply this technique in the preparation of Bell and…
Based on a `shortcut-to-adiabaticity' (STA) scheme, we theoretically design and experimentally realize a set of high-fidelity single-qubit quantum gates in a superconducting Xmon qubit system. Through a precise microwave control, the qubit is driven to follow a fast `adiabatic' trajectory with the assistance of a counter-diabatic field and the correction of derivative removal by adiabatic gates. The experimental measurements of quantum process tomography and interleaved randomized benchmarking show that the process fidelities of our STA quantum gates are higher than 94.9% and the gate fideliti…
We propose a protocol to realize fast high-fidelity quantum state transfer between distant optomechanical interfaces connected by a continuum waveguide. The scheme consists of three steps: two accelerating adiabatic processes joined by a population conversion process. In comparison to the traditional adiabatic technique, our method reaches a higher transfer fidelity with a shorter time. Numerical results show that the fidelity of this transfer scheme in the dissipative system mainly depends on the protocol speed and the coupling strength of the waveguide and cavities. Assisted by inverting the…
Ground-state cooling of mechanical resonators is an important task in quantum optomechanics, because it is a necessary prerequisite for creation, manipulation, and application of macroscopic mechanical coherence. Here, we propose a transient-state scheme to accelerate ground-state cooling of a mechanical resonator in a three-mode loop-coupled optomechanical system via shortcuts to adiabaticity (STA). We consider four kinds of coupling protocols and calculate the evolution of the mean phonon number of the mechanical resonator in both the adiabatic and STA cases. We verify that the ground-state …
With the advent of quantum technologies, control issues are becoming increasingly important. In this article, we address the control in phase space under a global constraint provided by a minimal energy-like cost function and a local (in Fourier space) constraint resulting from a robustness criterion. The inverse engineering Lagrangian formalism developed here generalizes the one commonly used to describe the superoscillation phenomenon. It is applied to both non-dissipative and dissipative quantum mechanics, and extended to stochastic thermodynamics. Interestingly, our approach also allows to…
High-fidelity quantum gates are essential for large-scale quantum computation. However, any quantum manipulation will inevitably affected by noises, systematic errors and decoherence effects, which lead to infidelity of a target quantum task. Therefore, implementing high-fidelity, robust and fast quantum gates is highly desired. Here, we propose a fast and robust scheme to construct high-fidelity holonomic quantum gates for universal quantum computation based on resonant interaction of three-level quantum systems via shortcuts to adiabaticity. In our proposal, the target Hamiltonian to induce …
