Quantum circuit design of discrete signal transforms using their fast computation flow graphs

In this paper, quantum circuit designs of discrete signal transforms are investigated. These signal transforms include discrete Fourier transform (DFT), discrete Hartley transform (DHT) and discrete cosine transform (DCT). The proposed design procedure can be divided into the following three steps. First, the signal transform matrices are decomposed into the product of sparse matrices based on their fast computation flow graphs. Second, each sparse matrix is implemented by elementary quantum gates. Third, the circuits for sparse matrices are cascaded to obtain the final circuit. The design results are compared with those of conventional design methods to demonstrate the effectiveness of the proposed design method in terms of quantum gate count.