Predicting properties of Scrooge ensembles with high accuracy and low sample complexity

arXiv:2609.39992 · quant-ph, cond-mat.stat-mech, math-ph, math.MP · Submitted 2026-09-30 · Read on arXiv

quant-ph, cond-mat.stat-mech, math-ph, math.MP

Submitted: 2026-09-30

Updated: 2026-10-02

Terminology

• Block Encoding — 44× in this paper · explained in 4 episodes
• Accuracy — 16× in this paper · explained in 1 episode
• Trace — 16× in this paper · explained in 2 episodes
• Post-Selection — 12× in this paper · explained in 2 episodes
• Ancilla Qubits — 9× in this paper · explained in 1 episode
• Hilbert Space — 9× in this paper · explained in 2 episodes
• Benchmarking — 6× in this paper · explained in 3 episodes
• Deep Thermalization — 6× in this paper · explained in 2 episodes
• Sample Complexity — 5× in this paper · explained in 15 episodes
• Shadow Tomography — 5× in this paper · explained in 4 episodes
• Quantum Circuits — 4× in this paper · explained in 2 episodes
• Gibbs State — 3× in this paper · explained in 2 episodes
• Ancillary Qubits — 1× in this paper · explained in 1 episode
• Bayesian Inference — 1× in this paper · explained in 5 episodes
• Chaotic Dynamics — 1× in this paper · explained in 2 episodes
• Entanglement — 1× in this paper · explained in 3 episodes
• Fidelity — 1× in this paper · explained in 2 episodes
• Generalization — 1× in this paper · explained in 13 episodes
• Phase Transitions — 1× in this paper · explained in 2 episodes
• Physical Constraints — 1× in this paper · explained in 7 episodes
• Query Complexity — 1× in this paper · explained in 2 episodes
• Unitary Dynamics — 1× in this paper · explained in 2 episodes

Sources

• Black Hole Information
• The Scrooge ensemble in many-body quantum systems
• Nature is stingy: Universality of Scrooge ensembles in quantum many-body systems
• Deep thermalization and Hilbert space ergodicity
• Emergence of the Scrooge Ensemble in the Sachdev-Ye-Kitaev Model
• Conditional dependence and Scrooge ensembles in shallow random quantum circuits
• Exact Hilbert-space ergodicity from continuous monitoring
• Applications of coherent classical communication and the Schur transform to quantum information theory
• The Church of the Symmetric Subspace
• Hamiltonian Simulation Using Linear Combinations of Unitary Operations

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