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Quantum Simulation

A Quantum Bluestein's Algorithm for Arbitrary-Size Quantum Fourier Transform

arXiv
Authors: Nan-Hong Kuo, Renata Wong

Year

2025

Paper ID

6003

Status

Preprint

Abstract Read

~2 min

Abstract Words

115

Citations

N/A

Abstract

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 = 2m 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.

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  • This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
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  • We propose a quantum analogue of Bluestein's algorithm (QBA) that implements an exact N-point Quantum Fourier Transform (QFT) for arbitrary N.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2512.15349 [2] arXiv https://arxiv.org/abs/2512.15349 [3] Publisher https://arxiv.org/abs/2512.15349

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