Advantage of Sample Complexity in Quantum PAC Learning Requires Inverse Access to State-Preparation Unitaries

arXiv:2609.38403 · quant-ph, cs.LG, stat.ML · Submitted 2026-09-29 · Read on arXiv

quant-ph, cs.LG, stat.ML

Submitted: 2026-09-29

Updated: 2026-09-29

Terminology

• Trace — 37× in this paper · explained in 2 episodes
• Agnostic Learning — 25× in this paper · explained in 1 episode
• Ambient Dimension — 20× in this paper · explained in 1 episode
• Sample Complexity — 19× in this paper · explained in 15 episodes
• Accuracy — 16× in this paper · explained in 1 episode
• VC Dimension — 13× in this paper · explained in 2 episodes
• Hilbert Space — 11× in this paper · explained in 2 episodes
• Query Complexity — 8× in this paper · explained in 2 episodes
• Trace Distance — 7× in this paper · explained in 3 episodes
• Probably Approximately Correct — 5× in this paper
• Arbitrary Superpositions — 1× in this paper · explained in 1 episode
• Heisenberg Scaling — 1× in this paper · explained in 4 episodes
• Japan Science and Technology Agency — 1× in this paper
• Quantum Circuits — 1× in this paper · explained in 2 episodes

Sources

• On establishing learning separations between classical and quantum machine learning with classical data
• Exponential separations between classical and quantum learners
• Amplitude amplification and estimation require inverses
• Inverse-free quantum state estimation with Heisenberg scaling
• Conjugate queries can help
• Are controlled unitaries helpful?
• Applications of coherent classical communication and the Schur transform to quantum information theory

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