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:2610.26786

Fast Hubbard-Thouless Pumping with Local Counterdiabatic Driving

Alexander Chansky

quant-phSubmitted Oct 19, 2026• Announced Oct 20, 2026• 0 citations
v1 · Oct 19, 2026v2 · Oct 22, 2026
arXivHTMLPDF

Abstract

Counterdiabatic (CD) driving suppresses the excitations of fast protocols by adding an auxiliary Hamiltonian, but in many-body and topological systems the exact CD term is generally non-local and multi-body. We study this obstruction for Thouless pumping in the Rice-Mele model, first without and then with interactions. For noninteracting fermions, the exact CD term of the pump is non-local, but the variational framework of Sels and Polkovnikov yields accurate nearest-neighbor approximations. For the spinful Rice-Mele chain with onsite and nearest-neighbor repulsion, in the regime where the competition of the two interactions stabilizes quantized pumping, this approach fails: the infinite-temperature variational action only penalizes the CD amplitudes, and the resulting two-parameter nearest-neighbor term does not prevent the pump from breaking down when the cycle time is reduced from $50/t$ to $2/t$. We trace the failure to the structure of the exact many-body gauge potential, whose amplitude for each hop depends on the interaction energy that the hop costs. Resolving the nearest-neighbor currents by this energy, and fixing the coefficients with a ground-state-weighted action, gives a local ansatz with 14 coefficients that keeps the interacting pump quantized for cycle times $T=2/t$ and $T=1/t$, with an accuracy per site that does not degrade between rings of 8 and 12 sites.

Comments
PRB Preprint

Related papers

Variational counterdiabatic driving of the Hubbard model for ground-state preparation

Qing Xie, Kazuhiro Seki, Seiji Yunoki

Counterdiabatic (CD) protocols enable fast driving of quantum states by invoking an auxiliary adiabatic gauge potential (AGP) that suppresses transitions to excited states throughout the driving process. Usually, the full spectrum of the original unassisted Hamiltonian is a prerequisite for constructing the exact AGP, which implies that CD protocols are extremely difficult for many-body systems. Here, we apply a variational CD protocol recently proposed by Claeys et al. [Phys. Rev. Lett. 123, 090602 (2019)] to a two-component fermionic Hubbard model in one spatial dimension. This protocol engages an approximated AGP expressed as a series of nested commutators. We show that the optimal variational parameters in the approximated AGP satisfy a set of linear equations whose coefficients are given by the squared Frobenius norms of these commutators. We devise an exact algorithm that escapes the formidable iterative matrix-vector multiplications and evaluates the nested commutators and the CD Hamiltonian in analytic representations. We then examine the CD driving of the one-dimensional Hubbard model up to $L=14$ sites with driving order $l\ensuremath{\leqslant}3$. Our results demonstrate the usefulness of the variational CD protocol to the Hubbard model and permit a possible route towards fast ground-state preparation for many-body systems.

arXiv:2206.07597•Physical review. B./Physical review. B•Oct 28, 2022•22 citations

Stabilization of Hubbard-Thouless pumps through nonlocal fermionic repulsion

Javier Argüello-Luengo, Manfred J. Mark, Francesca Ferlaino +3 more

Thouless pumping represents a powerful concept to probe quantized topological invariants in quantum systems. We explore this mechanism in a generalized Rice-Mele Fermi-Hubbard model characterized by the presence of competing onsite and intersite interactions. Contrary to recent experimental and theoretical results, showing a breakdown of quantized pumping induced by the onsite repulsion, we prove that sufficiently large intersite interactions allow for an interaction-induced recovery of Thouless pumps. Our analysis further reveals that the occurrence of stable topological transport at large interactions is connected to the presence of a spontaneous bond-order-wave in the ground-state phase diagram of the model. Finally, we discuss a concrete experimental setup based on ultracold magnetic atoms in an optical lattice to realize the newly introduced Thouless pump. Our results provide a new mechanism to stabilize Thouless pumps in interacting quantum systems.

arXiv:2308.13375•Quantum•Mar 14, 2024•17 citations

Splitting of topological charge pumping in an interacting two-component fermionic Rice-Mele Hubbard model

Eric Bertok, Fabian Heidrich‐Meisner, Armando A. Aligia

A Thouless pump transports an integer amount of charge when pumping adiabatically around a singularity. We study the splitting of such a critical point into two separate critical points by adding a Hubbard interaction. Furthermore, we consider extensions to a spinful Rice-Mele model, namely, a staggered magnetic field or an Ising-type spin coupling, further reducing the spin symmetry. The resulting models additionally allow for the transport of a single charge in a two-component system of spinful fermions, whereas in the absence of interactions, zero or two charges are pumped. In the SU(2)-symmetric case, the ionic Hubbard model is visited once along pump cycles that enclose a single singularity. Adding a staggered magnetic field additionally transports an integer amount of spin while the Ising term realizes a pure charge pump. We employ real-time simulations in finite and infinite systems to calculate the adiabatic charge and spin transport, complemented by the analysis of gaps and the many-body polarization to confirm the adiabatic nature of the pump. The resulting charge pumps are expected to be measurable in finite-pumping speed experiments in ultracold atomic gases for which the $\mathrm{SU}(2)$ invariant version is the most promising path. We discuss the implications of our results for a related quantum-gas experiment by Walter et al. [arXiv:2204.06561].

arXiv:2204.14144•Physical review. B./Physical review. B•Jul 27, 2022•37 citations

Floquet-Engineering Counterdiabatic Protocols in Quantum Many-Body Systems

Pieter W. Claeys, Mohit Pandey, Dries Sels +1 more

Counterdiabatic (CD) driving presents a way of generating adiabatic dynamics at an arbitrary pace, where excitations due to nonadiabaticity are exactly compensated by adding an auxiliary driving term to the Hamiltonian. While this CD term is theoretically known and given by the adiabatic gauge potential, obtaining and implementing this potential in many-body systems is a formidable task, requiring knowledge of the spectral properties of the instantaneous Hamiltonians and control of highly nonlocal multibody interactions. We show how an approximate gauge potential can be systematically built up as a series of nested commutators, remaining well defined in the thermodynamic limit. Furthermore, the resulting CD driving protocols can be realized up to arbitrary order without leaving the available control space using tools from periodically driven (Floquet) systems. This is illustrated on few- and many-body quantum systems, where the resulting Floquet protocols significantly suppress dissipation and provide a drastic increase in fidelity.

arXiv:1904.03209•Physical Review Letters•Aug 30, 2019•211 citations

Experimental Realization of Shortcuts to Adiabaticity in a Nonintegrable Spin Chain by Local Counterdiabatic Driving

Hui Zhou, Yunlan Ji, Xinfang Nie +4 more

Counterdiabatic driving (CD) offers a fast and robust strategy to manipulate and prepare the quantum state in multibody systems. However, the exact CD term involving the spectral properties of the system is difficult to calculate and generally takes a complicated form for higher-dimensional complex systems. Recently, Sels and Polkovnikov [Proc. Natl. Acad. Sci. U. S. A. 114, E3909 (2017)] proposed a variational method to optimally approximate the CD term with no need for the full spectral information of the original Hamiltonian. Using a nuclear-magnetic-resonance setup, here we report an experimental demonstration of this method to construct available shortcuts to adiabaticity in a nonintegrable spin-$1/2$ chain via only local controls. In this process, the ground state of such a system is rapidly prepared and the final state fidelity is significantly increased compared with the traditional adiabatic method. Our experiments prove the feasibility of this variational method to design CD in practice, and thus it is a promising strategy for fast, high-fidelity quantum-state manipulation in complex and noisy quantum systems.

Physical Review Applied•Apr 23, 2020•41 citations

Rapid counter-diabatic sweeps in lattice gauge adiabatic quantum computing

Andreas Hartmann, Wolfgang Lechner

We present a coherent counter-diabatic quantum protocol to prepare ground states in the lattice gauge mapping of all-to-all Ising models (LHZ) with considerably enhanced final ground state fidelity compared to a quantum annealing protocol.We make use of a variational method to find approximate counter-diabatic Hamiltonians that has recently been introduced by Sels and Polkovnikov (2017 Proc.Natl.Acad.Sci.114 3909).The resulting additional terms in our protocol are time-dependent local onsite y-magnetic fields.These additional Hamiltonian terms do not increase the minimal energy gap, but instead compensate for the Berry curvature.A single free parameter is introduced which is optimized via classical updates.The protocol consists only of local and nearest-neighbor terms which makes it attractive for implementation in near term experiments.

arXiv:1807.02053•New Journal of Physics•Mar 29, 2019•52 citations
Counterdiabatic (CD) driving suppresses the excitations of fast protocols by adding an auxiliary Hamiltonian, but in many-body and topological systems the exact CD term is generally non-local and multi-body. We study this obstruction for Thouless pumping in the Rice-Mele model, first without and then with interactions. For noninteracting fermions, the exact CD term of the pump is non-local, but the variational framework of Sels and Polkovnikov yields accurate nearest-neighbor approximations. For the spinful Rice-Mele chain with onsite and nearest-neighbor repulsion, in the regime where the competition of the two interactions stabilizes quantized pumping, this approach fails: the infinite-temperature variational action only penalizes the CD amplitudes, and the resulting two-parameter nearest-neighbor term does not prevent the pump from breaking down when the cycle time is reduced from 50/t50/t50/t to 2/t2/t2/t. We trace the failure to the structure of the exact many-body gauge potential, whose amplitude for each hop depends on the interaction energy that the hop costs. Resolving the nearest-neighbor currents by this energy, and fixing the coefficients with a ground-state-weighted action, gives a local ansatz with 14 coefficients that keeps the interacting pump quantized for cycle times T=2/tT=2/tT=2/t and T=1/tT=1/tT=1/t, with an accuracy per site that does not degrade between rings of 8 and 12 sites.
Counterdiabatic (CD) protocols enable fast driving of quantum states by invoking an auxiliary adiabatic gauge potential (AGP) that suppresses transitions to excited states throughout the driving process. Usually, the full spectrum of the original unassisted Hamiltonian is a prerequisite for constructing the exact AGP, which implies that CD protocols are extremely difficult for many-body systems. Here, we apply a variational CD protocol recently proposed by Claeys et al. [Phys. Rev. Lett. 123, 090602 (2019)] to a two-component fermionic Hubbard model in one spatial dimension. This protocol engages an approximated AGP expressed as a series of nested commutators. We show that the optimal variational parameters in the approximated AGP satisfy a set of linear equations whose coefficients are given by the squared Frobenius norms of these commutators. We devise an exact algorithm that escapes the formidable iterative matrix-vector multiplications and evaluates the nested commutators and the CD Hamiltonian in analytic representations. We then examine the CD driving of the one-dimensional Hubbard model up to L=14L=14L=14 sites with driving order $l\ensuremath{\leqslant}3$. Our results demonstrate the usefulness of the variational CD protocol to the Hubbard model and permit a possible route towards fast ground-state preparation for many-body systems.
Thouless pumping represents a powerful concept to probe quantized topological invariants in quantum systems. We explore this mechanism in a generalized Rice-Mele Fermi-Hubbard model characterized by the presence of competing onsite and intersite interactions. Contrary to recent experimental and theoretical results, showing a breakdown of quantized pumping induced by the onsite repulsion, we prove that sufficiently large intersite interactions allow for an interaction-induced recovery of Thouless pumps. Our analysis further reveals that the occurrence of stable topological transport at large interactions is connected to the presence of a spontaneous bond-order-wave in the ground-state phase diagram of the model. Finally, we discuss a concrete experimental setup based on ultracold magnetic atoms in an optical lattice to realize the newly introduced Thouless pump. Our results provide a new mechanism to stabilize Thouless pumps in interacting quantum systems.
A Thouless pump transports an integer amount of charge when pumping adiabatically around a singularity. We study the splitting of such a critical point into two separate critical points by adding a Hubbard interaction. Furthermore, we consider extensions to a spinful Rice-Mele model, namely, a staggered magnetic field or an Ising-type spin coupling, further reducing the spin symmetry. The resulting models additionally allow for the transport of a single charge in a two-component system of spinful fermions, whereas in the absence of interactions, zero or two charges are pumped. In the SU(2)-symmetric case, the ionic Hubbard model is visited once along pump cycles that enclose a single singularity. Adding a staggered magnetic field additionally transports an integer amount of spin while the Ising term realizes a pure charge pump. We employ real-time simulations in finite and infinite systems to calculate the adiabatic charge and spin transport, complemented by the analysis of gaps and the many-body polarization to confirm the adiabatic nature of the pump. The resulting charge pumps are expected to be measurable in finite-pumping speed experiments in ultracold atomic gases for which the SU(2)\mathrm{SU}(2)SU(2) invariant version is the most promising path. We discuss the implications of our results for a related quantum-gas experiment by Walter et al. [arXiv:2204.06561].
Counterdiabatic (CD) driving presents a way of generating adiabatic dynamics at an arbitrary pace, where excitations due to nonadiabaticity are exactly compensated by adding an auxiliary driving term to the Hamiltonian. While this CD term is theoretically known and given by the adiabatic gauge potential, obtaining and implementing this potential in many-body systems is a formidable task, requiring knowledge of the spectral properties of the instantaneous Hamiltonians and control of highly nonlocal multibody interactions. We show how an approximate gauge potential can be systematically built up as a series of nested commutators, remaining well defined in the thermodynamic limit. Furthermore, the resulting CD driving protocols can be realized up to arbitrary order without leaving the available control space using tools from periodically driven (Floquet) systems. This is illustrated on few- and many-body quantum systems, where the resulting Floquet protocols significantly suppress dissipation and provide a drastic increase in fidelity.
Counterdiabatic driving (CD) offers a fast and robust strategy to manipulate and prepare the quantum state in multibody systems. However, the exact CD term involving the spectral properties of the system is difficult to calculate and generally takes a complicated form for higher-dimensional complex systems. Recently, Sels and Polkovnikov [Proc. Natl. Acad. Sci. U. S. A. 114, E3909 (2017)] proposed a variational method to optimally approximate the CD term with no need for the full spectral information of the original Hamiltonian. Using a nuclear-magnetic-resonance setup, here we report an experimental demonstration of this method to construct available shortcuts to adiabaticity in a nonintegrable spin-1/21/21/2 chain via only local controls. In this process, the ground state of such a system is rapidly prepared and the final state fidelity is significantly increased compared with the traditional adiabatic method. Our experiments prove the feasibility of this variational method to design CD in practice, and thus it is a promising strategy for fast, high-fidelity quantum-state manipulation in complex and noisy quantum systems.
We present a coherent counter-diabatic quantum protocol to prepare ground states in the lattice gauge mapping of all-to-all Ising models (LHZ) with considerably enhanced final ground state fidelity compared to a quantum annealing protocol.We make use of a variational method to find approximate counter-diabatic Hamiltonians that has recently been introduced by Sels and Polkovnikov (2017 Proc.Natl.Acad.Sci.114 3909).The resulting additional terms in our protocol are time-dependent local onsite y-magnetic fields.These additional Hamiltonian terms do not increase the minimal energy gap, but instead compensate for the Berry curvature.A single free parameter is introduced which is optimized via classical updates.The protocol consists only of local and nearest-neighbor terms which makes it attractive for implementation in near term experiments.