  To overcome the difficulty of realizing large-scale quantum Fourier transform
(QFT) within existing technology, this paper presents a resource-saving method,
namely t-bit semiclassical QFT over (Z_(2^n)), which could realize large-scale
QFT using arbitrary-scale quantum register. Using our method, the scale of
quantum register can be determined flexibility according to the scale of
quantum system, enabling the quantum resource and speed of realizing QFT to be
optimal. By developing a feasible method to realize the control quantum gate
R_k, we experimentally demonstrate the 2-bit semiclassical QFT over (Z_(2^3))
on IBM's quantum cloud computer, showing the feasibility of our proposed
method. Then, we compare the actual performance of 2-bit semiclassical QFT and
standard QFT in the experiments. Experimental data show that the fidelity of
the result of 2-bit semiclassical QFT is higher than that of standard QFT,
which is mainly due to less two-qubit controlled gates are required in the
semiclassical QFT. Furthermore, based on the proposed method, we successfully
implement the Shor's algorithm to factorize N=15.
