The QFT maps computational basis states to frequency domain — the quantum analog of the discrete Fourier transform, exponentially faster.
Period Finding: QFT extracts periodicities from quantum states — key subroutine in Shor's algorithm for factoring integers.
Phase Estimation: Determines eigenvalues of unitary operators with exponential precision — foundation for quantum chemistry simulations.
Hidden Subgroup: Generalizes Deutsch-Jozsa, Simon, and Shor into a unified framework using QFT over groups.