Paired quantum Fourier transform with log 2 N Hadamard gates

摘要: The quantum Fourier transform (QFT) is perhaps the furthermost central building block in creation algorithms. In this work, we present a new approach to compute standard of length \( N = 2^{r} , \;r > 1 \), which also called r-qubit discrete transform. presented algorithm based on paired developed by authors. It shown that signal-flow graphs algorithms could be used for calculating and Hadamard with minimum number stages. calculation all components transforms performed gates matrices rotations simple NOT gates. presentation allows implementing QFT (a) using only r (b) organizing parallel computation Also, circuits length-2r fast are described. Several mathematical illustrative examples order 4,\;8 16 cases illustrated. Finally, inputs being two, three four qubits described detail.