Emergence of Universal Randomness in Quantum Many-body Dynamics
summary
Claim: natural many‑body dynamics produce universal pure‑state ensembles — projected ensembles show deep thermalization and, at infinite effective temperature, become approximate k‑designs. Rigorous results prove typical states and solvable models (kicked Ising: subsystem size NA ≤ t yields arbitrary k‑design in the thermodynamic limit; tuned 2D evolution maps to cluster‑state MBQC) meet this. Numerics show moments k=1–4 approach Haar with saturation values shrinking exponentially in total system size. Finite‑temperature ensembles follow a Scrooge ensemble; temporal ensembles equal a random‑phase model and their fluctuations give Porter‑Thomas statistics. Application: a generalized XEB benchmark for analog devices is implemented on a 60‑atom Rydberg simulator and a 10‑qubit superconducting device and reproduces fidelity estimates.
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chapters (6)
- 0:00Emergent universal randomness
- 3:22Quantum many-body systems
- 9:26Projected ensemble properties
- 24:11Temporal ensemble universality
- 32:42Benchmarking quantum devices
- 40:09Summary and future
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