Near-Optimal Separations of Certificate Complexity from Randomized and Quantum Query Complexity

arXiv:2609.11664 · quant-ph · Submitted 2026-09-10 · Read on arXiv

quant-ph

Submitted: 2026-09-10

Updated: 2026-10-05

Project page: https://arriopolis.github.io/docs/complexity-theory-table.pdf

Terminology

• Query Complexity — 20× in this paper · explained in 2 episodes
• Verification — 18× in this paper · explained in 2 episodes
• Accuracy — 1× in this paper · explained in 1 episode
• Geometric Distribution — 1× in this paper · explained in 2 episodes
• Large Language Model (LLM) — 1× in this paper · explained in 3 episodes

Sources

• Separations in query complexity using cheat sheets
• Degree vs. Approximate Degree and Quantum Implications of Huang's Sensitivity Theorem
• Improved Algorithm and Lower Bound for Variable Time Quantum Search
• Quantum Amplitude Amplification and Estimation
• Bounds for Small-Error and Zero-Error Quantum Algorithms
• Exact quantum query complexity for total Boolean functions
• Optimal Unambiguous DNFs and Alon-Saks-Seymour

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