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Title: Transitionless driving on adiabatic search algorithm

Abstract

We study quantum dynamics of the adiabatic search algorithm with the equivalent two-level system. Its adiabatic and non-adiabatic evolution is studied and visualized as trajectories of Bloch vectors on a Bloch sphere. We find the change in the non-adiabatic transition probability from exponential decay for the short running time to inverse-square decay in asymptotic running time. The scaling of the critical running time is expressed in terms of the Lambert W function. We derive the transitionless driving Hamiltonian for the adiabatic search algorithm, which makes a quantum state follow the adiabatic path. We demonstrate that a uniform transitionless driving Hamiltonian, approximate to the exact time-dependent driving Hamiltonian, can alter the non-adiabatic transition probability from the inverse square decay to the inverse fourth power decay with the running time. This may open up a new but simple way of speeding up adiabatic quantum dynamics.

Authors:
 [1];  [1]
  1. Qatar Environment and Energy Research Institute, Qatar Foundation, Doha (Qatar)
Publication Date:
OSTI Identifier:
22423767
Resource Type:
Journal Article
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 141; Journal Issue: 22; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9606
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; APPROXIMATIONS; ASYMPTOTIC SOLUTIONS; FUNCTIONS; HAMILTONIANS; PROBABILITY; QUANTUM STATES; TIME DEPENDENCE

Citation Formats

Oh, Sangchul, Kais, Sabre, and Department of Chemistry, Department of Physics and Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907. Transitionless driving on adiabatic search algorithm. United States: N. p., 2014. Web. doi:10.1063/1.4903451.
Oh, Sangchul, Kais, Sabre, & Department of Chemistry, Department of Physics and Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907. Transitionless driving on adiabatic search algorithm. United States. doi:10.1063/1.4903451.
Oh, Sangchul, Kais, Sabre, and Department of Chemistry, Department of Physics and Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907. Sun . "Transitionless driving on adiabatic search algorithm". United States. doi:10.1063/1.4903451.
@article{osti_22423767,
title = {Transitionless driving on adiabatic search algorithm},
author = {Oh, Sangchul and Kais, Sabre and Department of Chemistry, Department of Physics and Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907},
abstractNote = {We study quantum dynamics of the adiabatic search algorithm with the equivalent two-level system. Its adiabatic and non-adiabatic evolution is studied and visualized as trajectories of Bloch vectors on a Bloch sphere. We find the change in the non-adiabatic transition probability from exponential decay for the short running time to inverse-square decay in asymptotic running time. The scaling of the critical running time is expressed in terms of the Lambert W function. We derive the transitionless driving Hamiltonian for the adiabatic search algorithm, which makes a quantum state follow the adiabatic path. We demonstrate that a uniform transitionless driving Hamiltonian, approximate to the exact time-dependent driving Hamiltonian, can alter the non-adiabatic transition probability from the inverse square decay to the inverse fourth power decay with the running time. This may open up a new but simple way of speeding up adiabatic quantum dynamics.},
doi = {10.1063/1.4903451},
journal = {Journal of Chemical Physics},
issn = {0021-9606},
number = 22,
volume = 141,
place = {United States},
year = {2014},
month = {12}
}