  In a seminal paper[JHEP09(2007)120], Hayden and Preskill showed that
information can be retrieved from a black hole that is sufficiently scrambling,
assuming that the retriever has perfect control of the emitted Hawking
radiation and perfect knowledge of the internal dynamics of the black hole. In
this paper, we show that for $t-$doped Clifford black holes - that is, black
holes modeled by random Clifford circuits doped with an amount $t$ of
non-Clifford resources - an information retrieval decoder can be learned with
fidelity scaling as $\exp(-\alpha t)$ using quantum machine learning while
having access only to out-of-time-order correlation functions. We show that the
crossover between learnability and non-learnability is driven by the amount of
non-stabilizerness present in the black hole and sketch a different approach to
quantum complexity.
