Quantum Physics
This paper has been withdrawn by Ronit Shah
[Submitted on 19 Jan 2025 (v1), last revised 10 Feb 2025 (this version, v2)]
Title:A Faster Quantum Fourier Transform
No PDF available, click to view other formatsAbstract: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.
Submission history
From: Ronit Shah [view email][v1] Sun, 19 Jan 2025 06:18:52 UTC (6 KB)
[v2] Mon, 10 Feb 2025 05:05:17 UTC (1 KB) (withdrawn)
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