# Difference between semiclassical QFT and QFT

In papers, one of them being An Experimental Study of Shor's Factoring Algorithm on IBM Q is stated that replacing QFT with the semiclassical QFT (Kitaev's approach) reduces the needed number of qubits to solve a given problem with Shor's algorithm. Other than using a different approach - measuring one qubit of the period register each time contrary to the approach where multiple qubits are used is there a mathematical difference between sc-QFT and QFT?

More precisely, my question is: if QFT is mathematically described as

$$| x \rangle \rightarrow \frac{1}{\sqrt{N}} \sum_{y=0}^{N-1} \exp\left(\frac{2\pi ixy}{N}\right) | y\rangle,$$

how does the equation for sc-QFT look like?

• Did you try to read this one: arxiv.org/pdf/quant-ph/9511007.pdf? arxiv.org/pdf/quant-ph/0001066.pdf? They are references numner 12 and 13 in arxiv.org/pdf/1507.08852.pdf Jan 16, 2022 at 9:30
• Yes and all I can see is the equation I have stated rewritten in different forms. All I can conclude is that the sc-QFT is just another approach and not a different mathematical operator compared to QFT. However, as I'm not 100% sure of this I'm asking this question. Jan 17, 2022 at 13:52