Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2404.19013 · Physical review. B./Physical review. B

Transitionless quantum driving of the Tomonaga-Luttinger liquid

Léonce Dupays, Adolfo del Campo

Published Mar 19, 2025• 1 citation
arXivHTMLPDF

Abstract

Shortcuts to adiabaticity (STA) make the fast preparation of many-body states possible, circumventing the limitations of adiabatic strategies. We propose a fast STA protocol for generating interacting states in the Tomonaga-Luttinger liquid by counterdiabatic driving, stirring the dynamics with an auxiliary control field. To this end, we exploit the equivalence between the time-dependent Tomonaga-Luttinger liquid and an ensemble of quantum oscillators with driven mass and frequency. We specify the closed-form expression of the counterdiabatic control and demonstrate its efficiency in suppressing excitations.

DOI
10.1103/physrevb.111.l100303

Related papers

Exact dynamics of the Tomonaga-Luttinger liquid and shortcuts to adiabaticity

Léonce Dupays, Balázs Dóra, Adolfo del Campo

Controlling many-body quantum systems is a highly challenging task required to advance quantum technologies. Here, we report progress in controlling gapless many-body quantum systems described by the Tomonaga-Luttinger liquid (TLL). To do so, we investigate the exact dynamics of the TLL induced by an arbitrary interaction quench, making use of the SU ( 1 , 1 ) dynamical symmetry group and the Schrödinger picture. First, we demonstrate that this approach is useful to perform a shortcut to adiabaticity, which cancels the final nonadiabatic residual energy of the driven TLL and is experimentally implementable in the semiclassical limit of the sine-Gordon model. Second, we apply this framework to analyze various driving schemes in finite time, including linear ramps and smooth protocols. Published by the American Physical Society 2024

arXiv:2401.17884•Physical review. B./Physical review. B•Oct 3, 2024•3 citations

Adiabatic tracking of quantum many-body dynamics

Hamed Saberi, Tomáš Opatrný, Klaus Mølmer +1 more

The nonadiabatic dynamics of a many-body system driven through a quantum critical point can be controlled using counterdiabatic driving, where the formation of excitations is suppressed by assisting the dynamics with auxiliary multiple-body nonlocal interactions. We propose an alternative scheme which circumvents practical challenges to realize shortcuts to adiabaticity in mesoscopic systems by tailoring the functional form of the auxiliary counterdiabatic interactions. A driving scheme resorting in short-range few-body interactions is shown to generate an effectively adiabatic dynamics.

arXiv:1408.0524•Physical Review A•Dec 1, 2014•145 citations

Experimental preparation of Greenberger-Horne-Zeilinger states in an Ising spin model by partially suppressing the nonadiabatic transitions

Yunlan Ji, Ji Bian, Xi Chen +4 more

The creation of multipartite entangled states is a key task of quantum information processing. Among the various implementations, shortcut to adiabaticity (STA) offers a fast and robust means for generating entanglement. The traditional counterdiabatic driving, as a conventional and simple method for STA, suppresses transitions with an auxiliary Hamiltonian, but its complex interactions in many-body systems may hamper the feasibility of experimental implementation. To avoid this drawback, a flexible and efficient way was proposed theoretically by Chen et al. [Phys. Rev. A 93, 052109 (2016)] by substituting the counterdiabatic terms. Inspired by this work, we devise a practical protocol for preparing the Greenberger-Horne-Zeilinger state on the Ising spin model via STA by partial suppression of the nonadiabatic transitions, which can obviously reduce the complexity in experiments compared with the original method. We also experimentally demonstrate the viability of our scheme with a nuclear magnetic resonance quantum simulator. This work provides an alternative method to realize fast coherent quantum control for a multiqubit system in experiments.

Physical Review A•Mar 15, 2019•25 citations

Generating shortcuts to adiabaticity in quantum and classical dynamics

Christopher Jarzynski

Transitionless quantum driving achieves adiabatic evolution in a hurry, using a counterdiabatic Hamiltonian to stifle nonadiabatic transitions. Here this shortcut to adiabaticity is cast in terms of a generator of adiabatic transport. This yields a classical analog of transitionless driving, and provides a strategy for constructing quantal counterdiabatic Hamiltonians. As an application of this framework, exact classical and quantal counterdiabatic terms are obtained for a particle in a box and for even-power-law potentials in one degree of freedom.

arXiv:1305.4967•Physical Review A•Oct 4, 2013•159 citations

Fast adiabatic evolution by oscillating initial Hamiltonians

Francesco Petiziol, Benjamin Dive, Florian Mintert +1 more

We propose a method to produce fast transitionless dynamics for finite-dimensional quantum systems without requiring additional Hamiltonian components not included in the initial control setup, remaining close to the true adiabatic path at all times. The strategy is based on the introduction of an effective counterdiabatic scheme: a correcting Hamiltonian is constructed which approximatively cancels nonadiabatic effects, inducing an evolution tracking the adiabatic states closely. This can be absorbed into the initial Hamiltonian by adding a fast oscillation in the control parameters. We show that a consistent speedup can be achieved without requiring strong control Hamiltonians, using it both as a stand-alone shortcut to adiabaticity and as a weak correcting field. A number of examples are treated, dealing with quantum state transfer in avoided-crossing problems and entanglement creation.

arXiv:1807.10227•Physical Review A•Oct 31, 2018•58 citations

Shortcuts to Adiabaticity in Krylov Space

Kazutaka Takahashi, Adolfo del Campo

Shortcuts to adiabaticity provide fast protocols for quantum state preparation in which the use of auxiliary counterdiabatic controls circumvents the requirement of slow driving in adiabatic strategies. While their development is well established in simple systems, their engineering and implementation are challenging in many-body quantum systems with many degrees of freedom. We show that the equation for the counterdiabatic term—equivalently, the adiabatic gauge potential—is solved by introducing a Krylov basis. The Krylov basis spans the minimal operator subspace in which the dynamics unfolds and provides an efficient way to construct the counterdiabatic term. We apply our strategy to paradigmatic single- and many-particle models. The properties of the counterdiabatic term are reflected in the Lanczos coefficients obtained in the course of the construction of the Krylov basis by an algorithmic method. We examine how the expansion in the Krylov basis incorporates many-body interactions in the counterdiabatic term. Published by the American Physical Society 2024

arXiv:2302.05460•Physical Review X•Feb 28, 2024•50 citations
Shortcuts to adiabaticity (STA) make the fast preparation of many-body states possible, circumventing the limitations of adiabatic strategies. We propose a fast STA protocol for generating interacting states in the Tomonaga-Luttinger liquid by counterdiabatic driving, stirring the dynamics with an auxiliary control field. To this end, we exploit the equivalence between the time-dependent Tomonaga-Luttinger liquid and an ensemble of quantum oscillators with driven mass and frequency. We specify the closed-form expression of the counterdiabatic control and demonstrate its efficiency in suppressing excitations.
Controlling many-body quantum systems is a highly challenging task required to advance quantum technologies. Here, we report progress in controlling gapless many-body quantum systems described by the Tomonaga-Luttinger liquid (TLL). To do so, we investigate the exact dynamics of the TLL induced by an arbitrary interaction quench, making use of the SU ( 1 , 1 ) dynamical symmetry group and the Schrödinger picture. First, we demonstrate that this approach is useful to perform a shortcut to adiabaticity, which cancels the final nonadiabatic residual energy of the driven TLL and is experimentally implementable in the semiclassical limit of the sine-Gordon model. Second, we apply this framework to analyze various driving schemes in finite time, including linear ramps and smooth protocols. Published by the American Physical Society 2024
The nonadiabatic dynamics of a many-body system driven through a quantum critical point can be controlled using counterdiabatic driving, where the formation of excitations is suppressed by assisting the dynamics with auxiliary multiple-body nonlocal interactions. We propose an alternative scheme which circumvents practical challenges to realize shortcuts to adiabaticity in mesoscopic systems by tailoring the functional form of the auxiliary counterdiabatic interactions. A driving scheme resorting in short-range few-body interactions is shown to generate an effectively adiabatic dynamics.
The creation of multipartite entangled states is a key task of quantum information processing. Among the various implementations, shortcut to adiabaticity (STA) offers a fast and robust means for generating entanglement. The traditional counterdiabatic driving, as a conventional and simple method for STA, suppresses transitions with an auxiliary Hamiltonian, but its complex interactions in many-body systems may hamper the feasibility of experimental implementation. To avoid this drawback, a flexible and efficient way was proposed theoretically by Chen et al. [Phys. Rev. A 93, 052109 (2016)] by substituting the counterdiabatic terms. Inspired by this work, we devise a practical protocol for preparing the Greenberger-Horne-Zeilinger state on the Ising spin model via STA by partial suppression of the nonadiabatic transitions, which can obviously reduce the complexity in experiments compared with the original method. We also experimentally demonstrate the viability of our scheme with a nuclear magnetic resonance quantum simulator. This work provides an alternative method to realize fast coherent quantum control for a multiqubit system in experiments.
Transitionless quantum driving achieves adiabatic evolution in a hurry, using a counterdiabatic Hamiltonian to stifle nonadiabatic transitions. Here this shortcut to adiabaticity is cast in terms of a generator of adiabatic transport. This yields a classical analog of transitionless driving, and provides a strategy for constructing quantal counterdiabatic Hamiltonians. As an application of this framework, exact classical and quantal counterdiabatic terms are obtained for a particle in a box and for even-power-law potentials in one degree of freedom.
We propose a method to produce fast transitionless dynamics for finite-dimensional quantum systems without requiring additional Hamiltonian components not included in the initial control setup, remaining close to the true adiabatic path at all times. The strategy is based on the introduction of an effective counterdiabatic scheme: a correcting Hamiltonian is constructed which approximatively cancels nonadiabatic effects, inducing an evolution tracking the adiabatic states closely. This can be absorbed into the initial Hamiltonian by adding a fast oscillation in the control parameters. We show that a consistent speedup can be achieved without requiring strong control Hamiltonians, using it both as a stand-alone shortcut to adiabaticity and as a weak correcting field. A number of examples are treated, dealing with quantum state transfer in avoided-crossing problems and entanglement creation.
Shortcuts to adiabaticity provide fast protocols for quantum state preparation in which the use of auxiliary counterdiabatic controls circumvents the requirement of slow driving in adiabatic strategies. While their development is well established in simple systems, their engineering and implementation are challenging in many-body quantum systems with many degrees of freedom. We show that the equation for the counterdiabatic term—equivalently, the adiabatic gauge potential—is solved by introducing a Krylov basis. The Krylov basis spans the minimal operator subspace in which the dynamics unfolds and provides an efficient way to construct the counterdiabatic term. We apply our strategy to paradigmatic single- and many-particle models. The properties of the counterdiabatic term are reflected in the Lanczos coefficients obtained in the course of the construction of the Krylov basis by an algorithmic method. We examine how the expansion in the Krylov basis incorporates many-body interactions in the counterdiabatic term. Published by the American Physical Society 2024