Quantum Fourier Transform

The Quantum Fourier Transform (QFT) is a quantum algorithm that transforms a quantum state into its frequency components, similar to how a classical Fourier transform decomposes signals into sine and cosine waves. It operates on qubits to convert information from the time or spatial domain into the frequency domain, enabling quantum computers to efficiently analyze periodic patterns. QFT is fundamental in algorithms like Shor's for factoring large numbers, providing exponential speed-ups over classical methods. In essence, it leverages quantum superposition and interference to perform complex Fourier analysis more efficiently than traditional approaches.