Affiliation:
1. Information Science Teaching and Research Section, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China
2. College of Marxism, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China
Abstract
Quantum Fourier transform (QFT) transformation plays a very important role in the design of many quantum algorithms. Fractional Fourier transform (FRFT), as an extension of the Fourier transform, is particularly important due to the design of its quantum algorithm. In this paper, a new reformulation of the weighted fractional Fourier transform (WFRFT) is proposed in order to realize quantum FRFT; however, we found that this reformulation can be applied to other transformations, and therefore, this paper presents the weighted fractional Hartley transform (WFRHT). For the universality of application, we further propose a general weighted fractional-order transform (WFRT). When designing the quantum circuits, we realized the quantum WFRFT via QFT and quantum phase estimation (QPE). Moreover, after extending our design to the WFRHT, we were able to formulate the quantum WFRHT. Finally, in accordance with the research results, we designed the quantum circuit of the general WFRT, and subsequently proposed the quantum WFRT. The research in this paper has great value as a reference for the design and application of quantum algorithms.
Funder
Fundamental Research Funds for the Central Universities
Scientific Research Projects of Hebei colleges and universities
Subject
Statistics and Probability,Statistical and Nonlinear Physics,Analysis
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