Quantum Weighted Fractional-Order Transform

Quantum Fourier transform (QFT) transformation plays a very important role in the design of many quantum algorithms. Fractional (FRFT), as an extension transform, is particularly due to its algorithm. In this paper, new reformulation weighted fractional (WFRFT) proposed order realize FRFT; however, we found that can be applied other transformations, and therefore, paper presents Hartley (WFRHT). For universality application, further propose general fractional-order (WFRT). When designing circuits, realized WFRFT via QFT phase estimation (QPE). Moreover, after extending our WFRHT, were able formulate WFRHT. Finally, accordance with research results, designed circuit WFRT, subsequently WFRT. The has great value reference for application