  Scrambling processes, which rapidly spread entanglement through many-body
quantum systems, are difficult to investigate using standard techniques, but
are relevant to quantum chaos and thermalization. In this Letter, we ask if
quantum machine learning (QML) could be used to investigate such processes. We
prove a no-go theorem for learning an unknown scrambling process with QML,
showing that any variational ansatz is highly probable to have a barren plateau
landscape, i.e., cost gradients that vanish exponentially in the system size.
This implies that the required resources scale exponentially even when
strategies to avoid such scaling (e.g., from ansatz-based barren plateaus or
No-Free-Lunch theorems) are employed. Furthermore, we numerically and
analytically extend our results to approximate scramblers. Hence, our work
places generic limits on the learnability of unitaries when lacking prior
information.
