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- W4366732524 abstract "Black holes are conjectured to be the fastest scramblers of information in nature, with a scrambling time, $tau _{sc}$, that scales logarithmically with the number of degrees of freedom of the system, $tau _{sc} sim log n$. At the same time, recent work suggests that resolving some of the long-standing information paradoxes inherent in the quantum description of evaporating black holes requires cryptographic level scrambling of information. The implication is that black holes are effective generators of computational pseudorandomness, i.e., that they generate pseudorandom quantum states that cannot be distinguished from Haar-random by an observer with polynomial resources. The simple point made and explicitly justified in this paper is that, when analyzed in the context of universal $2$-qubit-gate-based random quantum circuits - which are generally employed as simple models of black hole dynamics - these two conjectures are inconsistent with one another. More precisely, we argue that $log n$-depth $2$-qubit-gate-based random quantum circuits that match the speed limit for scrambling, conjectured for black holes, cannot produce computationally pseudorandom quantum states. However, producing such states with shallow $log n$-depth quantum circuits ${it can}$ be accomplished if one employs universal families of ``inflationary'' quantum (IQ) gates implemented either as a subset of 2-qu$d$it-gates in $U(d^2)$ with $dge 3$ and $d$ prime, or as special 3-qubit gates." @default.
- W4366732524 created "2023-04-24" @default.
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- W4366732524 date "2023-04-19" @default.
- W4366732524 modified "2023-10-18" @default.
- W4366732524 title "Can black holes be both fast and thorough scramblers?" @default.
- W4366732524 doi "https://doi.org/10.48550/arxiv.2304.09885" @default.
- W4366732524 hasPublicationYear "2023" @default.
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