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Quantum Physics

arXiv:2501.12414 (quant-ph)
[Submitted on 19 Jan 2025]

Title:A Faster Quantum Fourier Transform

Authors:Ronit Shah
View a PDF of the paper titled A Faster Quantum Fourier Transform, by
Ronit Shah
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    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 $\Theta(n \log n)$ gates, and the exact
    in $\Theta(n^2)$ 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 $\Theta(n(\log \log n)^2)$ algorithm for the
    approximate QFT using $\Theta(\log n)$ ancillas, and an $\Theta(n
    (\log n)^2)$ algorithm for the exact QFT requiring $\Theta(n)$
    ancillas.

Subjects: Quantum Physics (quant-ph)
Cite as:  arXiv:2501.12414 [quant-ph]
          (or arXiv:2501.12414v1 [quant-ph] for this version)
          https://doi.org/10.48550/arXiv.2501.12414
          Focus to learn more
          arXiv-issued DOI via DataCite

Submission history

From: Ronit Shah [view email]
[v1] Sun, 19 Jan 2025 06:18:52 UTC (6 KB)
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