arXiv:2503.22212

Universal Defect Statistics in Counterdiabatic Quantum Critical Dynamics

András Grabarits, Adolfo del Campo

Published Mar 28, 2025• 0 citations

Abstract

Counterdiabatic driving (CD) provides a framework for suppressing excitations in nonadiabatic processes. Exact CD protocols require nonlocal control fields, and CD approximations with tailored locality are needed for their implementation. However, the performance of local CD schemes remains poorly understood. Here, we develop an analytically tractable local CD expansion scheme and establish a universal scaling theory governing the defect statistics after crossing a quantum phase transition as a function of the CD locality order. Our predictions are tested on the transverse field Ising model and long-range Kitaev models. Our results provide an analytical framework for evaluating the effectiveness of local CD protocols in quantum state preparation, control, and optimization.

DOI: 10.48550/arxiv.2503.22212

Related papers

Universal Counterdiabatic Driving in Krylov Space

Stewart Morawetz, Anatoli Polkovnikov

Local counterdiabatic (CD) driving provides a systematic way of constructing a control protocol to approximately suppress the excitations resulting from changing some parameter(s) of a quantum system at a finite rate. However, designing CD protocols typically requires knowledge of the original Hamiltonian . In this work, we design local CD driving protocols in Krylov space using only the characteristic local time scales of the system set by e.g., phonon frequencies in materials or Rabi frequencies in superconducting qubit arrays. Surprisingly, we find that convergence of these universal protocols is controlled by the asymptotic high-frequency tails of the response functions. This finding hints at a deep connection between the long-time, low-frequency response of the system controlling non-adiabatic effects, and the high-frequency response determined by the short-time operator growth and the Krylov complexity. We make this connection concrete by showing how, for a representative integrable model, we may extract long-time universal behavior of the correlation functions from a short-time expansion of the dynamics using a system-independent universal protocol.

arXiv:2503.01952PRX QuantumAug 26, 20259 citations

Efficient paths for local counterdiabatic driving

Stewart Morawetz, Anatoli Polkovnikov

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.

arXiv:2401.12287Physical review. B./Physical review. BJul 2, 202421 citations

Counterdiabatic Driving with Performance Guarantees

Jernej Rudi Finžgar, Simone Notarnicola, Madelyn Cain +2 more

Counterdiabatic (CD) driving has the potential to speed up adiabatic quantum state preparation by suppressing unwanted excitations. However, existing approaches either require intractable classical computations or are based on approximations that do not have performance guarantees. We propose and analyze a nonvariational, system-agnostic CD expansion method and analytically show that it converges exponentially quickly in the expansion order. In finite systems, the required resources scale inversely with the spectral gap, which we argue is asymptotically optimal. To extend our method to the thermodynamic limit and suppress errors stemming from high-frequency transitions, we leverage finite-time adiabatic protocols. In particular, we show that a time determined by the quantum speed limit is sufficient to prepare the desired ground state, without the need to optimize the adiabatic trajectory. Numerical tests of our method on the quantum Ising chain show that our method can outperform state-of-the-art variational CD approaches.

arXiv:2503.01958Physical Review LettersSep 24, 20258 citations

Quantum counterdiabatic driving enhanced by two-stage local control

Changhao Li, Jiayu Shen, Ruslan Shaydulin +1 more

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.

arXiv:2403.01854Communications PhysicsAug 27, 20261 citation

Fighting Exponentially Small Gaps by Counterdiabatic Driving

András Grabarits, Federico Balducci, Adolfo del Campo

We investigate the efficiency of approximate counterdiabatic driving (CD) in accelerating adiabatic passage through exponentially small gaps. First, we analyze a minimal spin-glass bottleneck model that is analytically tractable and exhibits both an exponentially small gap at the transition point and a change in the ground state that involves a macroscopic rearrangement of spins. Using the variational Floquet-Krylov expansion to construct CD terms, we find that while the formation of excitations is significantly suppressed, achieving a fully adiabatic evolution remains challenging. Extending our investigation to realistic NP-hard spin-glass problems—specifically, the 3-regular and 3-—we find again that local CD expansions lead to negligible improvements in the final ground-state fidelity. These results highlight the limited impact of local CD methods in overcoming the bottlenecks associated with first-order quantum phase transitions. To address this limitation, we propose an alternative method, termed quantum brachistochrone counterdiabatic driving (QBCD), which employs the approximate full CD connecting the ground state and the first-excited state at a single-parameter value close to the critical point. In the minimal spin-glass model, QBCD enables exponentially faster adiabatic evolution than the local strategies. To alleviate the challenges of its experimental and classical implementation for realistic -hard problems, we exponentially reduce the nonlocality of the QBCD Hamiltonian by sparsifying its matrix elements to the density of the local expansions. Despite this drastic simplification, sparsified QBCD maintains finite ground-state fidelity at driving times exponentially shorter than in local strategies and counterdiabatic optimized local driving, demonstrating that even an exponentially reduced fraction of nonlocality near the critical point is sufficient to achieve significant speedup across spin-glass bottlenecks. At the same time, reduced nonlocality facilitates classical implementations via advanced numerical methods, while on quantum hardware its truncation serves as a resource-efficient approximation scheme for higher-order CD realizations.

arXiv:2410.02520PRX QuantumNov 19, 20254 citations

Local Counterdiabatic Driving for Jaynes-Cummings Lattices

A. Govindarajan, Lin Tian

Jaynes-Cummings (JC) lattices can be constructed by connecting quantum two-level systems with cavities and have been widely studied for polariton many-body states and multipartite entanglement. Although adiabatic evolution has been studied for the generation of many-body states in this system, its reliance on long timescales can lead to serious decoherence. Here we present a scheme that utilizes local counterdiabatic (CD) driving to provide fast and high-fidelity state preparation in JC lattices. The exact CD Hamiltonian for this system contains nonlocal couplings between qubits and cavities at different and distant sites, which causes a challenge in the implementation. Leveraging the symmetries of the eigenstates under both periodic and open boundary conditions, we derive a local CD Hamiltonian that generates the same dynamics as the exact CD Hamiltonian and our numerical simulations confirm this result. We also show that a multipartite W-state can be prepared with high fidelity using this method. The implementation and decoherence of this scheme with superconducting quantum devices are also discussed.

arXiv:2409.19186Sep 27, 20240 citations