The complexity of learning (pseudo)random dynamics of black holes and other chaotic systems
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13130_2025_Article_25809.pdf
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Author(s)
Yang, Lisa
Engelhardt, Netta
Date Issued
March 20, 2025
Journal
Journal of High Energy Physics
Publisher
Springer Berlin Heidelberg
Citation
Yang, L., Engelhardt, N. The complexity of learning (pseudo)random dynamics of black holes and other chaotic systems. J. High Energ. Phys. 2025, 153 (2025).
Version
Final published version
Abstract
It has been recently proposed that the naive semiclassical prediction of non-unitary black hole evaporation can be understood in the fundamental description of the black hole as a consequence of ignorance of high-complexity information. Validity of this conjecture implies that any algorithm which is polynomially bounded in computational complexity cannot accurately reconstruct the black hole dynamics. In this work, we prove that such bounded quantum algorithms cannot accurately predict (pseudo)random unitary dynamics, even if they are given access to an arbitrary set of polynomially complex observables under this time evolution; this shows that “learning” a (pseudo)random unitary is computationally hard. We use the common simplification of modeling black holes and more generally chaotic systems via (pseudo)random dynamics. The quantum algorithms that we consider are completely general, and their attempted guess for the time evolution of black holes is likewise unconstrained: it need not be a linear operator, and may be as general as an arbitrary (e.g. decohering) quantum channel.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Center for Theoretical Physics
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DOI of Published Version
https://doi.org/10.1007/JHEP03(2025)153
