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

arXiv:2512.15349 · quant-ph · Submitted 2025-12-17 · Read on arXiv

quant-ph

Submitted: 2025-12-17

Updated: 2025-12-23

Code: https://github.com/renatawong/quantum-bluestein

Terminology

• Quantum Fourier Transform — 10× in this paper
• Hilbert Space — 4× in this paper · explained in 2 episodes
• Analyzer — 1× in this paper · explained in 1 episode
• Ancillary Qubits — 1× in this paper · explained in 1 episode
• Approximate Quantum Fourier Transform — 1× in this paper
• Core — 1× in this paper · explained in 2 episodes

Sources

• Fast Fourier transforms and fast Wigner and Weyl functions in large quantum systems
• An approximate Fourier transform useful in quantum factoring
• Optimal ancilla-free Clifford+T approximation of z-rotations
• Linear Depth Stabilizer and Quantum Fourier Transformation Circuits with no Auxiliary Qubits in Finite Neighbor Quantum Architectures
• Physics-Informed Support Vector Kernels via Green-Function Analogies and Jackson-Chebyshev Spectral Design

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