Barren plateaus preclude learning scramblers

Presenting Author: Zoe Holmes, Los Alamos National Laboratory
Contributing Author(s): Andrew Arrasmith, Bin Yan, Patrick J. Coles, Andreas Albrecht and Andrew T. Sornborger

Scrambling, the rapid spread of information through many-body quantum systems, is fundamental to a wide range of fields, from quantum chaos to thermalisation and black holes. However, given the complexity of many body quantum systems, scrambling can be hard to study using standard techniques. Recently, quantum machine learning (QML) has emerged as a promising 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 present a no-go theorem which restricts this possible use of QML. Specifically, we show that any QML approach used to learn the unitary dynamics implemented by a typical scrambler will exhibit a barren plateau, i.e. the cost gradient will vanish exponentially with the system size. As such, any QML algorithm to learn a scrambler will be untrainable. 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 initialization. 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 QML cannot be used to efficiently learn an unknown unitary process, placing a fundamental limit on QML.

Read this article online: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.126.190501

(Session 3 : Thursday from 2:30pm-2:50pm)


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