Quantum Algorithms on Edge Lists: Hiding, Shuffling, and Cycle Finding

arXiv:2412.17786 · quant-ph, cs.CC, cs.DS · Submitted 2024-12-23 · Read on arXiv

quant-ph, cs.CC, cs.DS

Submitted: 2024-12-23

Updated: 2026-05-28

Comments: 80 pages; v2: major update to include new results on cycle finding; v3: corrected Mirroring Lemma and improved presentation; v4: changed title and improved presentation

Journal ref: 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026), LIPIcs 374, 97:1-97:16 (2026)

DOI: 10.4230/LIPIcs.ICALP.2026.97

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Query Complexity — 74× in this paper · explained in 2 episodes
• Adjacency Matrix — 13× in this paper · explained in 1 episode
• ACM Symposium on Theory of Computing — 8× in this paper
• Adaptation — 5× in this paper · explained in 1 episode
• Consistency — 5× in this paper · explained in 3 episodes
• IEEE Symposium on Foundations of Computer Science — 4× in this paper
• ACM-SIAM Symposium on Discrete Algorithms — 2× in this paper
• Graph Construction — 2× in this paper · explained in 3 episodes
• Innovations in Theoretical Computer Science Conference — 2× in this paper
• Approximate Counting — 1× in this paper · explained in 1 episode
• Combinatorial Optimization — 1× in this paper · explained in 2 episodes
• Generalization — 1× in this paper · explained in 13 episodes
• Hypergraph — 1× in this paper · explained in 2 episodes
• Spectral Gap — 1× in this paper · explained in 5 episodes

Sources

• Tight Quantum Lower Bound for k-Distinctness
• Compressed Permutation Oracles
• The Compressed Oracle is a Worthy (Multiplicative) Adversary
• Adversary Lower Bound for Element Distinctness with Small Range
• Adversary Lower Bound for the Orthogonal Array Problem
• Quantum algorithms for hypergraph simplex finding

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