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Author Oh, Sangchul ♦ Kais, Sabre
Source United States Department of Energy Office of Scientific and Technical Information
Content type Text
Language English
Subject Keyword CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS ♦ ALGORITHMS ♦ APPROXIMATIONS ♦ ASYMPTOTIC SOLUTIONS ♦ FUNCTIONS ♦ HAMILTONIANS ♦ PROBABILITY ♦ QUANTUM STATES ♦ TIME DEPENDENCE
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.
ISSN 00219606
Educational Use Research
Learning Resource Type Article
Publisher Date 2014-12-14
Publisher Place United States
Journal Journal of Chemical Physics
Volume Number 141
Issue Number 22


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