Universal random statistics in quantum many-body systems and their applications

Here we find universal random statistics emerging from both temporal evolution and projective measurement, and study their applications. We experimentally uncover the signatures of these statistics with a Rydberg atom-array quantum simulator, revealing the emergence of the so-called Porter-Thomas distribution, a phenomenon which we find is universal across a wide variety of quantum computers and simulators. The presence of these statistics then allows further developments of recent protocols for quantum device benchmarking, with interesting applications for in situ Hamiltonian learning and closed-loop optimization of state preparation control, which we demonstrate. We then showcase benchmarking of a 33 qubit system, highlight possibilities for scaling this protocol to hundreds of qubits, and discuss prospects for realizing quantum advantage with near-term quantum simulators.