Training a decoder to retrieve information from a t-doped Clifford black hole

In a seminal paper[1], Hayden and Preskill showed that information can be retrieved from a black hole that is sufficiently scrambling provided that the retriever has total control over the emitted Hawking radiation and perfect knowledge of the internal dynamics of the black hole. In our work, we introduce a new quantum machine learning protocol that eliminates the latter requirement. We show that for t−doped Clifford unitaries - 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 decreasing exponentially in t using only out-of-time-order correlation functions. We show that the crossover between learnability and non-learnability is driven by the amount of non-Cliffordness in the black hole, demonstrating the link between non-stabilizerness and the onset of quantum chaos.

[1] P. Hayden and J. Preskill, Black holes as mirrors: quantum information in random subsystems, Journal of High Energy Physics 2007(09), 120 (2007), doi:10.1088/1126-6708/2007/09/120.