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

To overcome the difficulty of realizing large-scale quantum Fourier transform (QFT) within existing technology, this paper implements a resource-saving method (named t-bit semiclassical QFT over Z_2ⁿ), which could realize large-scale QFT using an arbitrary-scale quantum register. By developing a feasible method to realize the control quantum gate R_k, we experimentally realize the 2-bit semiclassical QFT over Z_2³ on IBM's quantum cloud computer, which shows the feasibility of the method. Then, we compare the actual performance of 2-bit semiclassical QFT with standard QFT in the experiments. The squared statistical overlap experimental data shows that the fidelity of 2-bit semiclassical QFT is higher than that of standard QFT, which is mainly due to fewer two-qubit gates in the semiclassical QFT. Furthermore, based on the proposed method, N=15 is successfully factorized by implementing Shor's algorithm.