Observable estimation in the absence of classical verification

Estimating observables is a central task in quantum simulation, and today's quantum processors can already implement circuits whose observable values lie beyond the reach of certified classical simulation. In this regime, only classical heuristics are available, raising a fundamental question: how do we build trust in the outcomes of quantum computation? In this talk, I will present an experimental study of operator dynamics in a family of structured circuits that challenge several leading classical simulation methods. We employ and compare observable estimates from multiple quantum experiments, using both heuristic and rigorous error-mitigation techniques, to establish confidence in the results of quantum simulation.