Quantum circuit design of 8x8 discrete fourier transform using its fast computation flow graph

In this paper, quantum circuit design of 8x8 discrete cosine transform (DCT) is investigated. The proposed design procedure can be divided into the following three steps. First, the DCT matrix is decomposed into the product of sparse matrices based on its fast computation flow graph. Second, each sparse matrix is implemented by elementary quantum gates. Third, cascade the circuits of sparse matrices to obtain the final circuit. The proposed method makes fast DCT computation algorithm in digital signal processing be suitable for implementation in quantum computer.