Multidimensional Quantum Fourier Transformation

• URL: http://arxiv.org/abs/2301.13835v1
• Date: Tue, 31 Jan 2023 18:25:40 GMT
• Title: Multidimensional Quantum Fourier Transformation
• Authors: Philipp Pfeffer
• Abstract summary: In this work, the known QFT circuit is used to derive an efficient circuit for the multidimensional QFT. An example on current hardware is depicted by a 6 qubit 2D-QFT with an IBM quantum computer.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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