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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.15349 |
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| _version_ | 1866917165455638528 |
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| 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 |