  Within the setting of the AdS/CFT correspondence, we ask about the power of
computers in the presence of gravity. We show that there are computations on
$n$ qubits which cannot be implemented inside of black holes with entropy less
than $O(2^n)$. To establish our claim, we argue computations happening inside
the black hole must be implementable in a programmable quantum processor, so
long as the inputs and description of the unitary to be run are not too large.
We then prove a bound on quantum processors which shows many unitaries cannot
be implemented inside the black hole, and further show some of these have short
descriptions and act on small systems. These unitaries with short descriptions
must be computationally forbidden from happening inside the black hole.
