Plain-Language Intuition
Imagine listening to a musical chord played on a piano.
To your ear, it's a complex sound wave vibrating together. But a musician with perfect pitch can instantly decompose that sound into individual notes (C, E, G).
The classical Discrete Fourier Transform (FFT) does this for signals, but testing N frequencies takes N·log(N) steps.
The Quantum Fourier Transform (QFT) transforms quantum amplitude waves across all 2ⁿ states in just O(n²) steps — an exponential speedup!
Instead of analyzing frequencies one by one, QFT maps computational numbers directly into the relative clock-face angles (phases) of your qubits.