Quantum state learning beyond approximate unitary designs

arXiv:2609.39994 · quant-ph · Submitted 2026-09-30 · Read on arXiv

quant-ph

Submitted: 2026-09-30

Updated: 2026-09-30

Terminology

• Trace — 23× in this paper · explained in 2 episodes
• Sample Complexity — 15× in this paper · explained in 15 episodes
• Fisher Information — 10× in this paper · explained in 3 episodes
• Accuracy — 9× in this paper · explained in 1 episode
• All-to-All Connectivity — 6× in this paper · explained in 1 episode
• Ancillary Qubits — 6× in this paper · explained in 1 episode
• Approximate Unitary t-design — 5× in this paper · explained in 1 episode
• Entanglement — 3× in this paper · explained in 4 episodes
• Hilbert Space — 3× in this paper · explained in 2 episodes
• National Research Foundation of Korea — 3× in this paper
• Benchmark — 2× in this paper · explained in 2 episodes
• Stabilizer States — 2× in this paper · explained in 2 episodes
• Additivity — 1× in this paper · explained in 1 episode
• Core — 1× in this paper · explained in 2 episodes
• Entanglement Entropy — 1× in this paper · explained in 2 episodes
• Hamming Distance — 1× in this paper · explained in 2 episodes
• No-Go Theorem — 1× in this paper · explained in 2 episodes
• Shadow Tomography — 1× in this paper · explained in 4 episodes

Sources

• Certifying localizable quantum properties with constant sample complexity
• The Clifford group forms a unitary 3-design
• Distributed Quantum Inner Product Estimation with Structured Random Circuits
• Quantum Nonlinear Properties from a Single Measurement Setting
• Complexity-driven transitions in quantum observation
• Strong random unitaries and fast scrambling
• Shallow randomized measurement in noisy quantum devices
• Sample-optimal single-copy quantum state tomography via shallow depth measurements
• Quantum Tomography From Few Full-Rank Observables
• Fast and robust quantum state tomography from few basis measurements
• Near-optimal quantum metrology with few-qubit measurements
• Single-copy stabilizer learning: average case and worst case
• Efficient decoding for the Hayden-Preskill protocol
• A New Lower Bound for Kullback-Leibler Divergence Based on Hammersley-Chapman-Robbins Bound

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• Theory of quantum-enhanced interferometry with general Markovian light sources
• A convergent hierarchy of spectral gap certificates for qubit Hamiltonians
• Universal Bound and Phase Transition in Many-Body Fermionic Non-Gaussianity