Counterdiabatic Driving with Performance Guarantees

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.