  Grover's algorithm is one of the most important quantum algorithms, which
performs the task of searching an unsorted database without a priori
probability. Recently the adiabatic evolution has been used to design and
reproduce quantum algorithms, including Grover's algorithm. In this paper, we
show that quantum search algorithm by adiabatic evolution has two properties
that conventional quantum search algorithm doesn't have. Firstly, we show that
in the initial state of the algorithm only the amplitude of the basis state
corresponding to the solution affects the running time of the algorithm, while
other amplitudes do not. Using this property, if we know a priori probability
about the location of the solution before search, we can modify the adiabatic
evolution to make the algorithm faster. Secondly, we show that by a factor for
the initial and finial Hamiltonians we can reduce the running time of the
algorithm arbitrarily. Especially, we can reduce the running time of adiabatic
search algorithm to a constant time independent of the size of the database.
The second property can be extended to other adiabatic algorithms.
