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Shortcuts to Adiabaticity
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Shortcuts to Adiabaticity

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Thermodynamics".

Deadline for manuscript submissions: closed (31 December 2020) | Viewed by 27096

Special Issue Editors

Prof. Dr. J. Gonzalo Muga

E-Mail Website
Guest Editor
Departamento de Química-Física, Facultad de Ciencias, UPV-EHU Apdo 644 Bilbao, Spain
Interests: quantum technologies; shortcuts to adiabaticity; non-Hermitian physics; time in quantum mechanics; trapped ions and cold atoms
Special Issues, Collections and Topics in MDPI journals
Prof. David Guéry-Odelin

E-Mail Website
Guest Editor
Laboratoire Collisions Agrégats Réactivité, Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
Interests: fast-forward; counterdiabatic driving; fast quantum control; out-of-equilibrium statistical physics; quantum transport
Dr. Andreas Ruschhaupt

E-Mail Website
Guest Editor
Department of Physics, University College Cork, T12 YN60 Cork, Ireland
Interests: quantum control; shortcuts to adiabaticity; quantum optics; time in quantum mechanics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Driving a system by slowly changing the control parameters guarantees, ideally, no excitations from the initial to the final setting, and the same final energies independent of the exact (smooth) trajectory of the parameters. Two main drawbacks of this ``adiabatic’’ approach are the length of time it takes and the fact that non-ideal, noisy conditions may spoil the intended outcome. Even so, adiabatic methods are ubiquitous in physics, chemistry, and engineering. 

Shortcuts to adiabaticity (STA) are a set of techniques to get the same results as the adiabatic methods in a short time, allowing for some transient excitations. The main approaches are based on invariants, fast-forward or counterdiabatic driving, inverse engineering, and local adiabatic methods, possibly hybridized with optimal control theory, perturbative, iterative, Lie-algebraic, and variational methods. Most of these approaches produce families of parameter paths, which can be used to optimize resilience with respect to noise and perturbations. Quantum physics has been the main application field, since the delicate quantum coherence is easily degraded in slow manipulations, but preserving it is essential to develop new quantum technologies. A further motivation is the possibility to produce microscopic engines or refrigerators that are both efficient and powerful. Other fields where STA are being applied are optics, to produce more compact devices; classical or stochastic mechanics; physical chemistry; and engineering.

Shortcuts play a very practical role, but also imply fundamental questions such as determining the trade-off relations and limits for process time, energy consumption, or information needed. This Special Issue will reflect the current, rich scenario of methods and applications of shortcuts to adiabaticity.

Prof. J. Gonzalo Muga
Prof. David Guéry-Odelin
Dr. Andreas Ruschhaupt
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • shortcuts to adiabaticity;
  • counterdiabatic driving;
  • invariant-based engineering;
  • fast-forward dynamics;
  • superadiabaticity;
  • cold atoms;
  • atom optics, superfluidity;
  • classical chaos;
  • quantum chaos;
  • quantum simulation;
  • quantum phase transition

Published Papers (10 papers)

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Research

13 pages, 1607 KiB  
Article
The Renewed Role of Sweep Functions in Noisy Shortcuts to Adiabaticity
by Michele Delvecchio, Francesco Petiziol and Sandro Wimberger
Entropy 2021, 23(7), 897; https://doi.org/10.3390/e23070897 - 14 Jul 2021
Cited by 1 | Viewed by 2320
Abstract
We study the robustness of different sweep protocols for accelerated adiabaticity following in the presence of static errors and of dissipative and dephasing phenomena. While in the noise-free case, counterdiabatic driving is, by definition, insensitive to the form of the original sweep function, [...] Read more.
We study the robustness of different sweep protocols for accelerated adiabaticity following in the presence of static errors and of dissipative and dephasing phenomena. While in the noise-free case, counterdiabatic driving is, by definition, insensitive to the form of the original sweep function, this property may be lost when the quantum system is open. We indeed observe that, according to the decay and dephasing channels investigated here, the performance of the system becomes highly dependent on the sweep function. Our findings are relevant for the experimental implementation of robust shortcuts-to-adiabaticity techniques for the control of quantum systems. Full article
(This article belongs to the Special Issue Shortcuts to Adiabaticity)
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22 pages, 1455 KiB  
Article
Connection between Inverse Engineering and Optimal Control in Shortcuts to Adiabaticity
by Qi Zhang, Xi Chen and David Guéry-Odelin
Entropy 2021, 23(1), 84; https://doi.org/10.3390/e23010084 - 09 Jan 2021
Cited by 14 | Viewed by 2363
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Shortcuts to Adiabaticity)
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13 pages, 399 KiB  
Article
Time-Rescaling of Dirac Dynamics: Shortcuts to Adiabaticity in Ion Traps and Weyl Semimetals
by Agniva Roychowdhury and Sebastian Deffner
Entropy 2021, 23(1), 81; https://doi.org/10.3390/e23010081 - 08 Jan 2021
Cited by 10 | Viewed by 2988
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Shortcuts to Adiabaticity)
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13 pages, 294 KiB  
Article
Shortcut-to-Adiabaticity-Like Techniques for Parameter Estimation in Quantum Metrology
by Marina Cabedo-Olaya, Juan Gonzalo Muga and Sofía Martínez-Garaot
Entropy 2020, 22(11), 1251; https://doi.org/10.3390/e22111251 - 03 Nov 2020
Cited by 7 | Viewed by 1972
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Shortcuts to Adiabaticity)
10 pages, 882 KiB  
Article
Digital Quantum Simulation of Nonadiabatic Geometric Gates via Shortcuts to Adiabaticity
by Yapeng Wang, Yongcheng Ding, Jianan Wang and Xi Chen
Entropy 2020, 22(10), 1175; https://doi.org/10.3390/e22101175 - 19 Oct 2020
Cited by 3 | Viewed by 2618
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Shortcuts to Adiabaticity)
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11 pages, 450 KiB  
Article
Shortcuts to Adiabaticity for Optical Beam Propagation in Nonlinear Gradient Refractive-Index Media
by Qian Kong, Huimin Ying and Xi Chen
Entropy 2020, 22(6), 673; https://doi.org/10.3390/e22060673 - 17 Jun 2020
Cited by 5 | Viewed by 2801
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Shortcuts to Adiabaticity)
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18 pages, 519 KiB  
Article
Nonadiabatic Energy Fluctuations of Scale-Invariant Quantum Systems in a Time-Dependent Trap
by Mathieu Beau and Adolfo del Campo
Entropy 2020, 22(5), 515; https://doi.org/10.3390/e22050515 - 30 Apr 2020
Cited by 6 | Viewed by 3101
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Shortcuts to Adiabaticity)
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15 pages, 519 KiB  
Article
Invariant-Based Inverse Engineering for Fast and Robust Load Transport in a Double Pendulum Bridge Crane
by Ion Lizuain, Ander Tobalina, Alvaro Rodriguez-Prieto and Juan Gonzalo Muga
Entropy 2020, 22(3), 350; https://doi.org/10.3390/e22030350 - 18 Mar 2020
Cited by 3 | Viewed by 3185
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Shortcuts to Adiabaticity)
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16 pages, 458 KiB  
Article
Noise Sensitivities for an Atom Shuttled by a Moving Optical Lattice via Shortcuts to Adiabaticity
by Xiao-Jing Lu, Andreas Ruschhaupt, Sofía Martínez-Garaot and Juan Gonzalo Muga
Entropy 2020, 22(3), 262; https://doi.org/10.3390/e22030262 - 25 Feb 2020
Cited by 17 | Viewed by 2603
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Shortcuts to Adiabaticity)
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14 pages, 529 KiB  
Article
Towards Generation of Cat States in Trapped Ions Set-Ups via FAQUAD Protocols and Dynamical Decoupling
by Mikel Palmero, Miguel Ángel Simón and Dario Poletti
Entropy 2019, 21(12), 1207; https://doi.org/10.3390/e21121207 - 09 Dec 2019
Cited by 4 | Viewed by 2012
Abstract
The high fidelity generation of strongly entangled states of many particles, such as cat states, is a particularly demanding challenge. One approach is to drive the system, within a certain final time, as adiabatically as possible, in order to avoid the generation of [...] Read more.
The high fidelity generation of strongly entangled states of many particles, such as cat states, is a particularly demanding challenge. One approach is to drive the system, within a certain final time, as adiabatically as possible, in order to avoid the generation of unwanted excitations. However, excitations can also be generated by the presence of dissipative effects such as dephasing. Here we compare the effectiveness of Local Adiabatic and the FAst QUasi ADiabatic protocols in achieving a high fidelity for a target superposition state both with and without dephasing. In particular, we consider trapped ions set-ups in which each spin interacts with all the others with the uniform coupling strength or with a power-law coupling. In order to mitigate the effects of dephasing, we complement the adiabatic protocols with dynamical decoupling and we test its effectiveness. The protocols we study could be readily implemented with state-of-the-art techniques. Full article
(This article belongs to the Special Issue Shortcuts to Adiabaticity)
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