Cyclotomic Cosets: Hidden Subgroup and Quantum Sieving Algorithm for Prime-Power Moduli

arXiv:2609.34996 · quant-ph, cs.CR · Submitted 2026-09-28 · Read on arXiv

quant-ph, cs.CR

Submitted: 2026-09-28

Updated: 2026-09-28

Terminology

• Quantum Fourier Transform — 19× in this paper
• Hidden Subgroup Problem — 12× in this paper
• Trace — 11× in this paper · explained in 2 episodes
• Learning With Errors — 10× in this paper
• Extrapolated Dihedral Coset Problem — 7× in this paper
• Cyclotomic Coset Problem — 6× in this paper
• Degeneracy — 2× in this paper · explained in 3 episodes
• Generalization — 2× in this paper · explained in 13 episodes
• Core — 1× in this paper · explained in 2 episodes
• Hilbert Space — 1× in this paper · explained in 2 episodes
• LWE to the Dihedral Coset Problem — 1× in this paper
• Sample Complexity — 1× in this paper · explained in 15 episodes

Sources

• A Note on Discrete Gaussian Combinations of Lattice Vectors
• Quantum Computing: Lecture Notes
• Quantum Fourier Transform Over Galois Rings

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