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Transitionless driving on adiabatic search algorithm.

Sangchul Oh1, Sabre Kais1

  • 1Qatar Environment and Energy Research Institute, Qatar Foundation, Doha, Qatar.

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Summary
This summary is machine-generated.

We investigated quantum dynamics in adiabatic search algorithms. A new method using transitionless driving can speed up quantum dynamics by altering transition probabilities.

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Area of Science:

  • Quantum physics
  • Quantum computation

Background:

  • Adiabatic quantum computation utilizes the adiabatic theorem to perform computations.
  • Understanding non-adiabatic transitions is crucial for algorithm efficiency.

Purpose of the Study:

  • To analyze quantum dynamics of the adiabatic search algorithm using a two-level system.
  • To investigate the impact of transitionless driving on non-adiabatic transition probabilities.

Main Methods:

  • Studying adiabatic and non-adiabatic evolution via Bloch vector trajectories on a Bloch sphere.
  • Deriving a transitionless driving Hamiltonian for the adiabatic search algorithm.
  • Analyzing the scaling of critical running time using the Lambert W function.

Main Results:

  • Non-adiabatic transition probability changes from exponential decay to inverse-square decay with running time.
  • Critical running time scales with the Lambert W function.
  • A uniform transitionless driving Hamiltonian changes non-adiabatic transition probability from inverse-square to inverse-fourth power decay.

Conclusions:

  • Transitionless driving offers a potential method for accelerating adiabatic quantum dynamics.
  • This approach provides a novel and simplified way to enhance quantum algorithm performance.