Quantum Fourier transform (QFT)

The quantum Fourier transform maps $|k⟩$ to $N^{-1/2}{\sum }_j{e}^{2\pi ijk/N}|j⟩$.

The Quantum Fourier Transform (QFT) is a quantum analogue of the classical discrete Fourier transform (DFT). It is a linear transformation that takes quantum states and transforms them into a superposition of frequencies, which is incredibly useful in various quantum algorithms, especially in algorithms for factoring integers and solving problems in quantum computing.