Multidimensional Quantum Fourier Transformation
The Quantum Fourier Transformation (QFT) is a well-known subroutine for
algorithms on qubit-based universal quantum computers. In this work, the known
QFT circuit is used to derive an efficient circuit for the multidimensional
QFT. The complexity of the algorithm is $\mathcal{O}( \log^2(M)/d )$ for an
array with $M=(2^n)^d$ elements $(n \in \mathbb{N})$ equally separated along
$d$ dimensions. Relevant properties for application are discussed. An example
on current hardware is depicted by a 6 qubit 2D-QFT with an IBM quantum
computer.
Philipp Pfeffer