Saved in:
Bibliographic Details
Main Authors: Kuo, Nan-Hong, Wong, Renata
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2512.15349
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866917165455638528
author Kuo, Nan-Hong
Wong, Renata
author_facet Kuo, Nan-Hong
Wong, Renata
contents We propose a quantum analogue of Bluestein's algorithm (QBA) that implements an exact $N$-point Quantum Fourier Transform (QFT) for arbitrary $N$. Our construction factors the $N$-dimensional QFT unitary into three diagonal quadratic-phase gates and two standard radix-2 QFT subcircuits of size $M = 2^m$ (with $M \ge 2N - 1$). This achieves asymptotic gate complexity $O((\log N)^2)$ and uses $O(\log N)$ qubits, matching the performance of a power-of-two QFT on $m$ qubits while avoiding the need to embed into a larger Hilbert space. We validate the correctness of the algorithm through a concrete implementation in Qiskit and classical simulation, confirming that QBA produces the exact $N$-point discrete Fourier transform on arbitrary-length inputs.
format Preprint
id arxiv_https___arxiv_org_abs_2512_15349
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A Quantum Bluestein's Algorithm for Arbitrary-Size Quantum Fourier Transform
Kuo, Nan-Hong
Wong, Renata
Quantum Physics
We propose a quantum analogue of Bluestein's algorithm (QBA) that implements an exact $N$-point Quantum Fourier Transform (QFT) for arbitrary $N$. Our construction factors the $N$-dimensional QFT unitary into three diagonal quadratic-phase gates and two standard radix-2 QFT subcircuits of size $M = 2^m$ (with $M \ge 2N - 1$). This achieves asymptotic gate complexity $O((\log N)^2)$ and uses $O(\log N)$ qubits, matching the performance of a power-of-two QFT on $m$ qubits while avoiding the need to embed into a larger Hilbert space. We validate the correctness of the algorithm through a concrete implementation in Qiskit and classical simulation, confirming that QBA produces the exact $N$-point discrete Fourier transform on arbitrary-length inputs.
title A Quantum Bluestein's Algorithm for Arbitrary-Size Quantum Fourier Transform
topic Quantum Physics
url https://arxiv.org/abs/2512.15349