4. QFT: Phase Estimation

Quantum Phase Estimation (QPE)

Many quantum algorithms rely on finding the eigenvalue of a unitary operator. If $U|\psi\rangle = e^{i heta}|\psi\rangle$, we want to estimate $ heta$.

The Quantum Fourier Transform (QFT) is the key. Just as a classical Fourier Transform extracts frequencies from a sound wave, the QFT extracts periodicity from quantum amplitudes.

QPE is the engine under the hood of most advanced quantum algorithms, including Shor's Algorithm and Quantum Chemistry simulations.