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  • Featured in Physics
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Universal Counterdiabatic Driving in Krylov Space

Stewart Morawetz* and Anatoli Polkovnikov

  • *Contact author: morawetz@bu.edu
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PRX Quantum 6, 040320 – Published 29 October, 2025

DOI: https://doi.org/10.1103/wbbs-s8fs

Abstract

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 a priori. 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.

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synopsis

A Shortcut to a Ground State

Published 29 October, 2025

Theorists have proposed a universal recipe for trying to quickly prepare a system in a desired ground state without exciting it.

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Popular Summary

Because of the rapid development of various platforms for quantum simulation, techniques that can be used to control them are required. One such approach is “counterdiabatic driving.” This can constrain a system to remain in its ground state even as its parameters are changed rapidly, at the expense of demanding greater control over the system. In this work, we find a systematic approach for constructing such approximate control protocols without any knowledge of the details of the system and demonstrate their efficacy in a variety of physically relevant systems.

A key advance in counterdiabatic driving was the development of a variational approach, where the best control protocol for a limited set of accessible controls can be obtained. Here, we observe that a natural basis for these approximate protocols enables one to perform this optimization without knowing the Hamiltonian. Then, one might expect the only relevant input to be the overall energy scale. Surprisingly, we find that the convergence of these universal protocols is not controlled by the low-energy, long-time behavior that is usually responsible for excitations in slowly driven systems. Instead, it is controlled by the response of the system to being driven at high frequency.

The method developed in this work might be applied to a practical quantum annealing problem, e.g., where disorder is present but not known. This work could also be a first step toward developing universal protocols that are particularly well suited for implementation in specific experimental platforms.

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Outline

Information

PRX Quantum 6, 040320– Published 29 October, 2025
  • Received 6 March 2025
  • Revised 8 July 2025
  • Accepted 26 August 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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