Simulation-Free Fidelity Estimation via Quantum Output Order Statistics

We introduce a simulation-free method to estimate the fidelity of large quantum circuits based on the order statistics of measured output probabilities from highly entangled, chaotic states. The approach requires only the highest-probability output bitstrings -- the most frequently observed measurement outcomes -- and builds on exact analytical results for the order statistics of Haar-random quantum states derived here. Analyzing their modification under depolarizing noise, we propose a scalable fidelity estimator, validated on Google's 12-qubit Sycamore experiment and further supported by numerical simulations. We demonstrate its practicality for intermediate-scale quantum circuits, where cross-entropy benchmarking is costly and direct fidelity estimation is difficult.