Noise-based operator weight spectroscopy for quantum dynamics

The dynamics of operator weight plays an important role in quantum many-body physics. It characterizes the scrambling of quantum information from local degrees of freedom into global ones, which is a key mechanism in quantum chaos and thermalization. However, it is typically hard to access directly in experiments. Here we propose to exploit the coupling between local depolarizing noise and operator weight in order to probe quantum information scrambling in a much more direct, noise-resilient manner. We consider different correlation functions in noisy random circuits and organize the contributions from all Pauli paths based on their total weight, thus defining a "weight spectrum". We show that the weight spectrum of the ideal dynamics can be extracted from noisy experimental data at variable noise strength. The weight spectrum can play a role similar to the "speckle pattern" of bitstring probabilities in random circuit sampling experiments: it has predictable statistical behavior over the ensemble of random circuits but can have unique features in each instance. This suggests a new route toward quantum advantage on noisy hardware.