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arXiv:2403.01854 · Communications Physics

Quantum counterdiabatic driving enhanced by two-stage local control

Changhao Li, Jiayu Shen, Ruslan Shaydulin, Marco Pistoia

Published Aug 27, 2026• 1 citation
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Abstract

Abstract Counterdiabatic driving can suppress diabatic losses during adiabatic ground state preparation. As its implementation necessitates the generation of an adiabatic gauge potential, which requires knowledge of the spectral gap of instantaneous Hamiltonians and involves highly non-local controls in many-body systems, local counterdiabatic driving with approximate adiabatic gauge potential has been widely adopted. In this work, using transverse-field Ising model as an example, we present an in-depth study of the performance of local counterdiabatic protocols and provide a closed-form analysis of ground-state-fidelity optimization. We then propose a two-stage protocol based on local counterdiabatic and simple local single-body control to further improve the performance. The practical implementation of these protocols does not require diagonalization of instantaneous Hamiltonians or spectral gaps, and only additional local single-body driving is involved. To benchmark their performance, we experimentally implement digitized adiabatic quantum evolution in a trapped-ion system. We characterize the quality of the prepared states and explore the scaling behavior with system size up to 14 qubits. Our demonstration of quantum shortcut to adiabaticity opens a path towards preparing ground states of complex systems with accessible local controls.

DOI
10.1038/s42005-026-02767-5

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Abstract Counterdiabatic driving can suppress diabatic losses during adiabatic ground state preparation. As its implementation necessitates the generation of an adiabatic gauge potential, which requires knowledge of the spectral gap of instantaneous Hamiltonians and involves highly non-local controls in many-body systems, local counterdiabatic driving with approximate adiabatic gauge potential has been widely adopted. In this work, using transverse-field Ising model as an example, we present an in-depth study of the performance of local counterdiabatic protocols and provide a closed-form analysis of ground-state-fidelity optimization. We then propose a two-stage protocol based on local counterdiabatic and simple local single-body control to further improve the performance. The practical implementation of these protocols does not require diagonalization of instantaneous Hamiltonians or spectral gaps, and only additional local single-body driving is involved. To benchmark their performance, we experimentally implement digitized adiabatic quantum evolution in a trapped-ion system. We characterize the quality of the prepared states and explore the scaling behavior with system size up to 14 qubits. Our demonstration of quantum shortcut to adiabaticity opens a path towards preparing ground states of complex systems with accessible local controls.
Local counterdiabatic driving (CD) provides a feasible approach for realizing approximate adiabatic or reversible processes like quantum state preparation using only local controls and without demanding excessively long protocol times. However, in many instances getting high accuracy of such CD protocols requires engineering very complicated new controls or pulse sequences. In this work, we describe a systematic method for altering the adiabatic path by adding extra local controls along which performance of local CD protocols is enhanced, both close to and far from the adiabatic limit. We also identify an iterative procedure to improve the performance of local counterdiabatic driving further without any knowledge of the quantum wave function. We then show that these methods provides dramatic improvement in the preparation of nontrivial Greenberger-Horne-Zeilinger ground states of several different spin systems with both short-range and long-range interactions.
A system undergoes adiabatic evolution when its population in the instantaneous eigenbasis of its time-dependent Hamiltonian changes only negligibly. The realization of such dynamics requires slow-enough changes of the parameters of the Hamiltonian, a task that can be hard to achieve near quantum critical points. A powerful alternative is provided by the counterdiabatic modification of the Hamiltonian allowing for an arbitrarily quick implementation of the adiabatic dynamics. Such a counterdiabatic driving protocol has been recently proposed for the quantum Ising model (del Campo et al 2012 Phys. Rev. Lett. 109 115703 ). We derive an exact closed-form expression for all the coefficients of the counterdiabatic Ising Hamiltonian. We discuss two approximations to the exact counterdiabatic Ising Hamiltonian quantifying their efficiency of the dynamical preparation of the desired ground state. In particular, these studies show how quantum criticality enhances finite-size effects in counterdiabatic dynamics.
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.
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.
Adiabatic protocols are employed across a variety of quantum technologies, from implementing state preparation and individual operations that are building blocks of larger devices, to higher-level protocols in quantum annealing and adiabatic quantum computation. The problem of speeding up these processes has garnered a large amount of interest, resulting in a menagerie of approaches, most notably quantum optimal control and shortcuts to adiabaticity. The two approaches are complementary: optimal control manipulates control fields to steer the dynamics in the minimum allowed time while shortcuts to adiabaticity aim to retain the adiabatic condition upon speed-up. We outline a new method which combines the two methodologies and takes advantage of the strengths of each. The new technique improves upon approximate local counterdiabatic driving with the addition of time-dependent control fields. We refer to this new method as counterdiabatic optimised local driving (COLD) and we show that it can result in a substantial improvement when applied to annealing protocols, state preparation schemes, entanglement generation and population transfer on a lattice. We also demonstrate a new approach to the optimisation of control fields which does not require access to the wavefunction or the computation of system dynamics. COLD can be enhanced with existing advanced optimal control methods and we explore this using the chopped randomised basis method and gradient ascent pulse engineering.
Adiabatic protocols are often employed in state preparation schemes but require the system to be driven by a slowly varying Hamiltonian so that transitions between instantaneous eigenstates are exponentially suppressed. Counterdiabatic driving is a technique to speed up adiabatic protocols by including additional terms calculated from the instantaneous eigenstates that counter diabatic excitations. However, this approach requires knowledge of the full eigenspectrum meaning that the exact analytical form of counterdiabatic driving is only known for a subset of problems, e.g., the harmonic oscillator and transverse field Ising model. We extend this subset of problems to include the general family of one-dimensional noninteracting lattice models with open boundary conditions and arbitrary onsite potential, tunneling terms, and lattice size. We will derive a general analytical form for the counterdiabatic term for all states of lattice models, including bound and in-gap states which appear, e.g., in topological insulators. We also derive the general analytical form of targeted counterdiabatic driving terms which are tailored to enforce the dynamical state to remain in a specific state. As an example of the use of the derived analytical forms, we consider state transfer using the topological edge states of the Su-Schrieffer-Heeger model. The derived analytical counterdiabatic driving Hamiltonian can be utilized to inform control protocols in many-body lattice models or to probe the nonequilibrium properties of lattice models. Published by the American Physical Society 2024