In a seminal paper [P. Hayden and J. Preskill, J. High Energy Phys. 09 (2007) 120, 10.1088/1126-6708/2007/09/120], 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(−α t ) using quantum machine learning while having access only to out-of-time-order correlation functions. We show that the crossover between learnability and nonlearnability is driven by the amount of nonstabilizerness present in the black hole and sketch a different approach to quantum complexity.