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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.

Realization of t -bit semiclassical quantum Fourier transform on IBM’s quantum cloud computer