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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.12414 |
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Table of Contents:
- 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.