On the Spectral theory of Isogeny Graphs and Quantum Sampling of Secure Supersingular Elliptic curves

arXiv:2602.02263 · quant-ph, math.NT · Submitted 2026-02-02 · Read on arXiv

quant-ph, math.NT

Submitted: 2026-02-02

Updated: 2026-09-21

Terminology

• Quantum Phase Estimation — 6× in this paper
• Adjacency Matrix — 4× in this paper · explained in 1 episode
• Verification — 4× in this paper · explained in 2 episodes
• Hilbert Space — 3× in this paper · explained in 2 episodes
• Trace — 3× in this paper · explained in 2 episodes
• Accuracy — 2× in this paper · explained in 1 episode
• Quantum Phase Estimation (QPE) — 2× in this paper · explained in 3 episodes
• Query Complexity — 1× in this paper · explained in 2 episodes
• Sparsity — 1× in this paper · explained in 4 episodes

Sources

• Quantum Money from Modular Forms
• The basis problem revisited
• The supersingular Endomorphism Ring and One Endomorphism problems are equivalent

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