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In automotive engineering, car suspension systems often employ Proportional Derivative (PD) controllers to enhance performance. PD controllers are utilized to adjust the damping force in response to road conditions. A controller, acting as an amplifier with a constant gain, demonstrates proportional control, with output directly mirroring input.
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Proportional-Derivative (PD) control is a widely used control method in various engineering systems to enhance stability and performance. In a system with only proportional control, common issues include high maximum overshoot and oscillation, observed in both the error signal and its rate of change. This behavior can be divided into three distinct phases: initial overshoot, subsequent undershoot, and gradual stabilization.
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Updated: Jan 11, 2026

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Counterdiabatic Driving with Performance Guarantees.

Jernej Rudi Finžgar1,2, Simone Notarnicola3,4,5, Madelyn Cain3

  • 1BMW AG, Munich, Germany.

Physical Review Letters
|November 17, 2025
PubMed
Summary
This summary is machine-generated.

We introduce a novel counterdiabatic (CD) driving method for faster quantum state preparation. This system-agnostic approach offers exponential convergence and outperforms existing techniques, even in complex quantum systems.

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Area of Science:

  • Quantum mechanics
  • Quantum computation
  • Quantum information science

Background:

  • Counterdiabatic (CD) driving accelerates adiabatic quantum state preparation by minimizing excitations.
  • Current CD methods often demand complex classical computations or rely on unproven approximations.

Purpose of the Study:

  • To develop a nonvariational, system-agnostic CD expansion method with guaranteed performance.
  • To analyze the convergence properties and resource scaling of the proposed method.
  • To extend the method for thermodynamic systems and high-frequency transitions.

Main Methods:

  • A nonvariational, system-agnostic CD expansion is proposed and analyzed.
  • Analytical demonstration of exponential convergence with expansion order.
  • Leveraging finite-time adiabatic protocols and quantum speed limit for thermodynamic systems.

Main Results:

  • The CD expansion method exhibits exponential convergence.
  • Resource requirements scale inversely with the spectral gap in finite systems.
  • The method effectively prepares ground states in the thermodynamic limit without trajectory optimization.
  • Numerical tests on the quantum Ising chain show superior performance compared to variational CD approaches.

Conclusions:

  • The proposed nonvariational CD method provides an efficient and robust approach to quantum state preparation.
  • It offers significant advantages over existing methods, particularly in terms of computational requirements and performance guarantees.
  • The method is scalable to the thermodynamic limit and applicable to various quantum systems.