2025/01/19 by Ronit Shah, R. Shah, Shah, Ronit · 6 voices
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #quant-ph
paper · pdf · doi:10.48550/arxiv.2501.12414
openalex publication_date 2025/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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(n2) 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.