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.
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14 December 2014
Research Article|
December 09 2014
Transitionless driving on adiabatic search algorithm
Sangchul Oh;
Sangchul Oh
a)
1
Qatar Environment and Energy Research Institute
, Qatar Foundation, Doha, Qatar
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Sabre Kais
Sabre Kais
b)
1
Qatar Environment and Energy Research Institute
, Qatar Foundation, Doha, Qatar
2Department of Chemistry, Department of Physics and Birck Nanotechnology Center,
Purdue University
, West Lafayette, Indiana 47907, USA
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a)
Email: soh@qf.org.qa
b)
Email: kais@purdue.edu
J. Chem. Phys. 141, 224108 (2014)
Article history
Received:
September 07 2014
Accepted:
November 24 2014
Citation
Sangchul Oh, Sabre Kais; Transitionless driving on adiabatic search algorithm. J. Chem. Phys. 14 December 2014; 141 (22): 224108. https://doi.org/10.1063/1.4903451
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