The power of oracle access: Optimal sample and query complexity of the abelian state hidden subgroup problem

arXiv:2609.35656 · quant-ph · Submitted 2026-09-28 · Read on arXiv

quant-ph

Submitted: 2026-09-28

Updated: 2026-09-28

Terminology

• Query Complexity — 34× in this paper · explained in 2 episodes
• Sample Complexity — 16× in this paper · explained in 15 episodes
• Generalization — 8× in this paper · explained in 13 episodes
• Hilbert Space — 7× in this paper · explained in 2 episodes
• Anticoncentration — 4× in this paper · explained in 1 episode
• Entanglement — 3× in this paper · explained in 3 episodes
• Annual ACM-SIAM Symposium on Discrete Algorithms — 2× in this paper
• Core — 2× in this paper · explained in 2 episodes
• Fidelity — 2× in this paper · explained in 2 episodes
• Adam — 1× in this paper · explained in 2 episodes
• Adaptive Sampling — 1× in this paper · explained in 1 episode
• Adaptivity — 1× in this paper · explained in 1 episode
• Algorithmic Primitives — 1× in this paper · explained in 1 episode
• All-to-All Connectivity — 1× in this paper · explained in 1 episode
• Quantum Circuits — 1× in this paper · explained in 2 episodes
• Quantum Singular Value Transformation (QSVT) — 1× in this paper · explained in 4 episodes
• Sparsity — 1× in this paper · explained in 4 episodes
• Trace — 1× in this paper · explained in 2 episodes
• Verification — 1× in this paper · explained in 2 episodes

Sources

• Quantum lower bounds by quantum arguments
• The Grand Challenge of Quantum Applications
• Compiling Quantum Regular Language States
• Variations on Quantum Adversary
• The state hidden subgroup problem and an efficient algorithm for locating unentanglement
• Quantum Amplitude Amplification and Estimation
• Quantum algorithm for a generalized hidden shift problem
• Demonstrating dynamic surface codes
• Mind the gaps: The fraught road to quantum advantage
• Quantum state isomorphism problems for groups
• Random purification channel made simple
• Efficient Learning of Structured Quantum Circuits via Pauli Dimensionality and Sparsity
• Quantum measurements and the Abelian Stabilizer Problem
• Learning T-conjugated stabilizers: The multiple-squares dihedral StateHSP
• Are controlled unitaries helpful?

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