|Author||Oh, Sangchul ♦ Kais, Sabre|
|Source||United States Department of Energy Office of Scientific and Technical Information|
|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.|
|Learning Resource Type||Article|
|Publisher Place||United States|
|Journal||Journal of Chemical Physics|
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