The Fourier transform is an important mathematical tool that decomposes a function or dataset into a its constituent frequencies, much like one could decompose a musical chord into a combination of its notes. It is used across all fields of engineering in some form or another and, accordingly, algorithms to compute it efficiently have been developed—that is, at least for conventional computers. But what about quantum computers?
Though quantum computing remains an enormous technical and intellectual challenge, it has the potential to speed up many programs and algorithms immensely, provided that appropriate quantum circuits are designed. In particular, the Fourier transform already has a quantum version called the quantum Fourier transform (QFT), but its applicability is quite limited because its results cannot be used in subsequent quantum arithmetic operations.
To address this issue, in a recent study published in Quantum Information Processing, scientists from Tokyo