Sharif Digital Repository

Adiabatic quantum algorithms are characterized by their run time and accuracy. The relation between the two is essential for quantifying adiabatic algorithmic performance yet is often poorly understood.We study the dynamics of a continuous time, adiabatic quantum search algorithm and find rigorous results relating the accuracy and the run time. Proceeding with estimates, we show that under fairly general circumstances the adiabatic algorithmic error exhibits a behavior with two discernible regimes: The error decreases exponentially for short times and then decreases polynomially for longer times.We show that the well-known quadratic speedup over classical search is associated only with the...