Year: 2025
Type: preprint
Abstract: We present an asymptotically improved algorithm for implementing the Quantum Fourier Transform (QFT) in both the exact and approximate settings. Historically, the approximate QFT has been implemented in $Θ(n \log n)$ gates, and the exact in $Θ(n^2)$ gates. In this work, we show that these costs can be reduced by leveraging a novel formulation of the QFT that recurses on two partitions of the qubits. Specifically, our approach yields an $Θ(n(\log \log n)^2)$ algorithm for the approximate QFT using $Θ(\log n)$ ancillas, and an $Θ(n(\log n)^2)$ algorithm for the exact QFT requiring $Θ(n)$ ancillas.
Source: arXiv (Cornell University)
Author: Shah, Ronit
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4406755575