Barren plateaus preclude learning scramblers

Scrambling, the process by which quantum information is rapidly spread through many-body quantum systems, has proven central not only to understanding quantum chaos but also to the study of the dynamics of quantum information, the black hole information paradox, random circuits and entropic uncertainty relations. However, the complexity of strongly-interacting many-body quantum systems makes scrambling rather challenging to study analytically. Recently, quantum machine learning (QML) has emerged as an exciting new paradigm for the study of complex physical processes. It is therefore natural to ask whether QML could be used to study scrambling. 

In this talk we will present a no-go theorem for the use of QML to study quantum scrambling. Namely, we show that any QML approach used to learn the unitary dynamics implemented by a typical scrambler will exhibit a barren plateau and thus be untrainable in the absence of further prior knowledge. Crucially, in contrast to previously established barren plateau phenomena, which are a consequence of the ansatz structure and parameter initialization strategy, our barren plateaus holds for any choice of ansatz and any initialization of parameters. Thus, previously proposed strategies for avoiding barren plateaus do not work here. 

More generally, given the close connection between scrambling and randomness, our no-go theorem also applies to learning random and pseudo-random unitaries. Consequently, our result implies that to efficiently learn an unknown unitary process using QML, prior information about that process is required. Thus, our result provides a fundamental limit on the domain of applicability of QML.