Deep thermalization and Hilbert space ergodicity

arXiv:2609.30248 · quant-ph, cond-mat.stat-mech · Submitted 2026-09-24 · Read on arXiv

quant-ph, cond-mat.stat-mech

Submitted: 2026-09-24

Updated: 2026-09-24

Comments: 11 pages, 5 figures. Comments welcome!

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Deep Thermalization — 51× in this paper · explained in 2 episodes
• Hilbert Space — 23× in this paper · explained in 2 episodes
• Entanglement — 10× in this paper · explained in 4 episodes
• Benchmarking — 7× in this paper · explained in 4 episodes
• Quantum Circuits — 7× in this paper · explained in 2 episodes
• Conservation Laws — 4× in this paper · explained in 3 episodes
• Phase Transitions — 4× in this paper · explained in 2 episodes
• Trace — 4× in this paper · explained in 2 episodes
• Generalization — 3× in this paper · explained in 13 episodes
• Gibbs State — 3× in this paper · explained in 2 episodes
• Chaotic Dynamics — 2× in this paper · explained in 2 episodes
• Physical Constraints — 2× in this paper · explained in 7 episodes
• Adam — 1× in this paper · explained in 2 episodes
• Entanglement Entropy — 1× in this paper · explained in 2 episodes
• Fidelity — 1× in this paper · explained in 2 episodes
• Post-Selection — 1× in this paper · explained in 2 episodes
• Quantum fluctuations — 1× in this paper · explained in 2 episodes
• Resource Constraints — 1× in this paper · explained in 4 episodes
• Sample Complexity — 1× in this paper · explained in 20 episodes
• Singapore National Research Foundation — 1× in this paper
• Stabilizer States — 1× in this paper · explained in 3 episodes
• Trace Distance — 1× in this paper · explained in 3 episodes

Sources

• Strategic Plan for Neutral Atom Quantum Computation
• Maximum entropy distributions of wavefunctions at thermal equilibrium
• Non-equilibrium theory of projected ensembles
• Quantum t-designs: t-wise independence in the quantum world
• High-temperature thermalization implies the emergence of quantum state designs
• Projected state ensemble of a generic model of many-body quantum chaos
• Deep thermalization with and without quantum chaos
• State $k$-designs from Hamiltonian evolution
• Sustained growth of quantum circuit complexity in many-body Hamiltonian dynamics
• Conditional dependence and Scrooge ensembles in shallow random quantum circuits
• Emergence of the Scrooge Ensemble in the Sachdev-Ye-Kitaev Model
• The Scrooge ensemble in many-body quantum systems
• Nature is stingy: Universality of Scrooge ensembles in quantum many-body systems
• Unraveling the emergence of quantum state designs in systems with symmetry
• Locality of deep thermalisation through the lens of entanglement teleportation
• Projected logical ensembles in surface codes via the random-matrix theory of quantum dots

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