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.affiliation: Qatar Environment and Energy Research Institute, Qatar Foundation, Doha, Qatar.
authors.forename: Sangchul
authors.initials: S
authors.lastname: Oh
authors.affiliation: Qatar Environment and Energy Research Institute, Qatar Foundation, Doha, Qatar.
authors.forename: Sabre
authors.initials: S
authors.lastname: Kais