Barren plateaus preclude learning scramblers

TL;DR

This paper proves that quantum machine learning cannot efficiently learn quantum scrambling processes due to barren plateau landscapes, establishing fundamental limits on the learnability of such complex quantum dynamics.

Contribution

It provides a no-go theorem showing that variational quantum algorithms face exponential resource scaling when learning scrambling processes, highlighting inherent limitations.

Findings

Barren plateaus cause exponential vanishing of gradients in learning scramblers.

Theoretical and numerical evidence extend results to approximate scramblers.

Limits on learnability of quantum unitaries without prior information are established.

Abstract

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.