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Black Holes and Complexity Classes
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It is not known what the limitations are on using quantum computation to speed up classical computation. An example would be the power to speed up PSPACE-complete computations. It is also not known what the limitations are on the duration of time over which classical general relativity can describe the interior geometry of black holes. What is known is that these two questions are closely connected: the longer GR can describe black holes, the more limited are quantum computers. This conclusion, formulated as a theorem, is a result of unpublished work done by Scott Aaronson and myself which I explain here.
Forward citations
Cited by 3 Pith papers
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Certifying localizable quantum properties with constant sample complexity
A new framework certifies global quantum properties including multipartite entanglement, circuit complexity, and quantum magic on small subsystems with constant sample complexity via local Pauli measurements.
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The arithmetic geometry of AdS$_2$ and its continuum limit
The paper constructs a continuum limit of the finite modular geometry AdS2[Z_N] by embedding it in a two-cutoff family and taking the two cutoffs to infinity along k-Fibonacci sequences.
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Probing the Black Hole Interior with Holographic Entanglement Entropy and the Role of AdS/BCFT Correspondence
The paper's central claim, that a Horndeski-gravity residual entropy -ξ/6 identifies smooth-interior microstates and firewalls, is an unsupported interpretation of previously derived formulas.
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