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  • Open Access

Improving Variational Counterdiabatic Driving with Weighted Actions and Computer Algebra

Naruo Ohga1,2,* and Takuya Hatomura2,3

  • 1Department of Physics, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
  • 2Basic Research Laboratories, NTT, Inc., Kanagawa 243-0198, Japan
  • 3NTT Research Center for Theoretical Quantum Information, NTT, Inc., Kanagawa 243-0198, Japan

  • *Contact author: naruo.ohga@ubi.s.u-tokyo.ac.jp
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PRX Quantum 7, 020347 – Published 2 June, 2026

DOI: https://doi.org/10.1103/rmsy-nypw

Abstract

Variational counterdiabatic (CD) driving is a disciplined and widely used method to robustly control quantum many-body systems by mimicking adiabatic processes with high fidelity and reduced duration. Central to this technique is a universal structure of the adiabatic gauge potential (AGP) over a parameterized Hamiltonian. Here, we reveal that introducing a new degree of freedom into the theory of the AGP can significantly improve variational CD driving. Specifically, we find that the algebraic characterization of the AGP is not unique, and we exploit this nonuniqueness to develop the weighted variational method for deriving a refined driving protocol. This approach extends the conventional method in two aspects: it assigns customized weights to matrix elements relevant to specific problems, and it effectively incorporates nonlocal information into local driving coefficients. We also develop an efficient numerical algorithm to compute the refined driving protocol using computer algebra. Our framework is broadly applicable and, in principle, it can replace any previous use of variational CD driving. We demonstrate its practicality by applying it to adiabatic evolution along the ground state of a parameterized Hamiltonian. This proposal outperforms the conventional method in terms of fidelity, as confirmed by extensive numerical simulations on quantum Ising models.

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Popular Summary

Quantum technology is an emerging field that harnesses the principles of quantum mechanics to perform useful real-world tasks. One of its central components is the technique for accurately and reliably controlling quantum systems. While this has been achieved fairly well for small systems, controlling large quantum systems—which are necessary for complicated, realistic tasks—remains a major challenge. We address this issue by significantly improving a method known as variational counterdiabatic (CD) driving.

Variational CD driving is a widely used method, but its control quality is still insufficient to realize practical quantum technologies with large and complex systems. To improve this method, we revisit and refine the theory of the adiabatic gauge potential—a core mathematical concept behind variational CD driving—and use it to develop an improved method called weighted variational CD driving. This finding is supplemented by a newly developed classical algorithm to efficiently apply our method to large quantum systems. Our proposal can boost the fidelity—the success probability of a process—by an order of magnitude, representing a substantial and practical improvement.

This proposal is expected to be used in a wide range of systems in the future. It can be applied to existing setups by replacing just one step of the conventional method with the “weighted” version. Due to its simplicity and scalability, the method has broad potential applications, including efficient quantum heat engines, reliable quantum information processing, and fast quantum computation.

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PRX Quantum 7, 020347– Published 2 June, 2026
  • Received 26 September 2025
  • Revised 16 January 2026
  • Accepted 3 April 2026
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