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Multidimensional Quantum Fourier Transformation
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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.
Forward citations
Cited by 3 Pith papers
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A Quantum Algorithm for Solving the Poisson Equation for Free Field Conditions via the Hockney Method
A QFT-based quantum Poisson solver with the Hockney method for free fields works in small ideal simulations, but the multiplication and state-preparation steps destroy any runtime advantage.
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A Spectral Quantum Algorithm for Numerical Differentiation and Integration
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