Experimental signatures of Hilbert-space ergodicity: Universal bitstring distributions and applications in noise learning

Understand

Systems reaching thermal equilibrium are ubiquitous.

• For classical systems, this phenomenon is typically understood statistically through ergodicity in phase space, but translating this to quantum systems is a long-standing problem of interest.
• Recently a strong notion of quantum ergodicity has been proposed, namely that isolated, global quantum states uniformly explore their available state space, dubbed Hilbert-space ergodicity.
• Here we observe signatures of this process with an experimental Rydberg quantum simulator and various numerical models, before generalizing to the case of a local quantum system interacting with its environment.