  The adiabatic quantum computation is a universal and robust method of quantum
computing. In this architecture, the problem can be solved by adiabatically
evolving the quantum processor from the ground state of a simple initial
Hamiltonian to that of a final one, which encodes the solution of the problem.
By far, there is no experimental realization of adiabatic quantum computation
on a single solid spin system under ambient conditions, which has been proved
to be a compatible candidate for scalable quantum computation. In this letter,
we report on the first experimental realization of an adiabatic quantum
algorithm on a single solid spin system under ambient conditions. All elements
of adiabatic quantum computation, including initial state preparation,
adiabatic evolution, and final state readout, are realized experimentally. As
an example, we factored 35 into its prime factors 5 and 7 on our adiabatic
quantum processor.
