Quantum Algorithm for unscrambling quantum information

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 our work, we show that for t−doped Clifford black holes - that are, black holes modeled by random Clifford circuits polluted with an amount t of non-Clifford resources - a randomized Clifford decoder can be learned using an algorithm requiring O(poly(n)exp(t)) queries access to the t-doped Clifford black hole. Decoder that, with probability 1-2^t-2n_C, retrieves the information with fidelity ≥ 1-2^n_A+t-2n_D. Consequently, with a suitable choice of n_C and n_D, one can retrieve the information scrambled by O(n)-doped Clifford circuits with overwhelming probability.