Synthetic quantum simulation experiments provide detailed probes to complex quantum many-body phenomena. In this talk, I will discuss how universal statistical principles and emergent randomness manifest in such experiments, offering theoretical insights and enabling novel benchmarking protocols.
The first part discusses random pure state ensembles that arise naturally in quantum simulators during unitary evolution or projective measurements. These ensembles obey a maximum entropy principle, subject to constraints such as energy conservation and thermalization, and are connected to phenomena like “Hilbert-space ergodicity” and “Deep thermalization”.
In the second part, I show how these theoretical results underpin fidelity benchmarking protocols for a 60-atom Rydberg quantum simulator operating in a regime inaccessible to exact classical simulations. I present results for fidelity and entanglement estimation, demonstrating the simulator’s ability to faithfully generate highly entangled quantum states.
Laboratory for Theoretical and Computational Physics