2.9 - QFT on Real-Valued Data, QFT Complexity and invQFT

The lecture slides are available here Download here.

This video lecture explores the Quantum Fourier Transform (QFT) concept applied to real-valued data and its complexity compared to the Fast Fourier Transform (FFT).

We explain the DFT's output and properties, such as mirror-image peaks in frequency space for real signals. The distinction between real and complex input signals in DFT and QFT is highlighted. The possibility of preparing entirely real signals for QFT is discussed, demonstrating a mirror-image effect similar to DFT. The lecture also touches on square wave signals and their phase-encoded characteristics before and after applying QFT.  Finally, we discuss the computational efficiency of QFT compared to FFT, showcasing its growth in complexity as a function of qubit states.  The inverse QFT (invQFT) is introduced as a tool for preparing periodically varying register superpositions.