Median Filtering of Quantum Signal Based on the Fractional Representation Model

In the past decade, quantum signal representation models based on quantum mechanics have produced some important results. However, researches on quantum signal processing is lagging behind, including the filtering of quantum signals. First, the fixed-point number quantum representation of digital signals (QRDS) proposed by Li Panchi et al. was improved, so that it is more suitable for time signals with any length. Then, a median filtering method was introduced based on the improved model, which avoids the drawback that quantum computing cannot directly implement convolution operations. To implement the quantum circuit of this filtering method, the basic quantum operation modules including comparator module, swap module and median calculation module were given in this paper. Finally, the effectiveness and rationality of the filtering method proposed in the paper were verified by examples.