Barren Plateaus Preclude Learning Scramblers

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