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A. May, Quantum tasks in holography
Original
1902
Earlier work this paper cites.
A. May, G. Penington, and J. Sorce, Holographic scattering requires a connected entanglement wedge
Original
1912
Earlier work this paper cites.
N. Tomczak-Jaegermann, The moduli of smoothness and convexity and the rademacher averages of the trace classes S p
1974
Earlier work this paper cites.
M. A. Nielsen and I. L. Chuang, Programmable quantum gate arrays
1997
Earlier work this paper cites.
C. H. Bennett, E. Bernstein, G. Brassard, and U. Vazirani, Strengths and weaknesses of quantum computing
Original
1997
Earlier work this paper cites.
N. Margolus and L. B. Levitin, The maximum speed of dynamical evolution
1998
Earlier work this paper cites.
R. Bousso, A covariant entropy conjecture
1999
Earlier work this paper cites.
E. E. Flanagan, D. Marolf, and R. M. Wald, Proof of classical versions of the Bousso entropy bound and of the generalized second law
2000
Earlier work this paper cites.
M. Sipser, Introduction to theory of computation
2004
Earlier work this paper cites.
S. Lloyd and Y. J. Ng, Black hole computers
2004
Earlier work this paper cites.

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2023

Kubicki, Aleksander M., May, Alex, Pérez-Garcia, David

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.

A. May, Quantum tasks in holography
Original
1902
Earlier work this paper cites.
A. May, G. Penington, and J. Sorce, Holographic scattering requires a connected entanglement wedge
Original
1912
Earlier work this paper cites.
N. Tomczak-Jaegermann, The moduli of smoothness and convexity and the rademacher averages of the trace classes S p
1974
Earlier work this paper cites.
M. A. Nielsen and I. L. Chuang, Programmable quantum gate arrays
1997
Earlier work this paper cites.
C. H. Bennett, E. Bernstein, G. Brassard, and U. Vazirani, Strengths and weaknesses of quantum computing
Original
1997
Earlier work this paper cites.
N. Margolus and L. B. Levitin, The maximum speed of dynamical evolution
1998
Earlier work this paper cites.
R. Bousso, A covariant entropy conjecture
1999
Earlier work this paper cites.
E. E. Flanagan, D. Marolf, and R. M. Wald, Proof of classical versions of the Bousso entropy bound and of the generalized second law
2000
Earlier work this paper cites.
M. Sipser, Introduction to theory of computation
2004
Earlier work this paper cites.
S. Lloyd and Y. J. Ng, Black hole computers
2004
Earlier work this paper cites.

S. Ishizaka and T. Hiroshima, Asymptotic teleportation scheme as a universal programmable quantum processor
Original
2008
Cited alongside, same era.
C. Akers and G. Penington, Leading order corrections to the quantum extremal surface prescription
Original
2008
Cited alongside, same era.
R. Bousso, H. Casini, Z. Fisher, and J. Maldacena, Proof of a quantum Bousso bound
2014
Cited alongside, same era.
N. Engelhardt and A. C. Wall, Quantum extremal surfaces: holographic entanglement entropy beyond the classical regime
2015
Cited alongside, same era.
S. P. Jordan, Fast quantum computation at arbitrarily low energy
2017
Cited alongside, same era.

J. Cotler, P. Hayden, G. Penington, G. Salton, B. Swingle, and M. Walter, Entanglement wedge reconstruction via universal recovery channels
Original
2019
Later among the works it cites.
A. R. Brown, H. Gharibyan, G. Penington, and L. Susskind, The python’s lunch: geometric obstructions to decoding hawking radiation
2020
Later among the works it cites.
N. Engelhardt, G. Penington, and A. Shahbazi-Moghaddam, A world without pythons would be so simple
2021
Later among the works it cites.
A. M. Kubicki, Local Banach space theory and resource quantification in quantum information processing
2021
Later among the works it cites.
A. May, Holographic quantum tasks with input and output regions
Original
2021
Later among the works it cites.