Computational complexity and black hole horizons

By L. Susskind. 2014

921 citations recorded by the source corpus.

Computational complexity is essential to understanding the properties of black hole horizons. The problem of Alice creating a firewall behind the horizon of Bob's black hole is a problem of computational complexity. In general we find that while creating firewalls is possible, it is extremely difficult and probably impossible for black holes that form in sudden collapse, and then evaporate. On the other hand if the radiation is bottled up then after an exponentially long period of time firewalls may be common. It is possible that gravity will provide tools to study problems of complexity; especially the range of complexity between scrambling and exponential complexity.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/3d8d8010dc5c59f6321af3b81edc999130abdfa7

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

1. R. Myers
2. D. Stanford
3. Shira Chapman
4. H. Marrochio
5. D. Harlow
6. J. Maldacena
7. L. Susskind
8. Phil Saad

In Nuclear and High Energy Physics

1. R. Myers
2. Shira Chapman
3. H. Marrochio
4. D. Stanford
5. T. Takayanagi
6. D. Harlow
7. J. Maldacena
8. Phil Saad

In Statistical and Nonlinear Physics

1. R. Myers
2. D. Stanford
3. Shira Chapman
4. H. Marrochio
5. D. Harlow
6. T. Takayanagi
7. Phil Saad
8. J. Maldacena

Citations in the corpus

• Comments on holographic complexity (2016, methodology): “These coefficients also contain dimensionless parameters characterizing the underlying CFT, e.g., CT ∼ Ld−1/GN in the present case where the bulk is described by Einstein gravity.11 The leading divergence appearing with the CV duality is proportional to the volume of the boundary time slice, i.e., C”
• Quantum chaos and the complexity of spread of states (2022, positive): “In chaotic systems, we found a linear growth of complexity for exponential time, followed by a plateau, as expected from the conjecture in [12], and further extended the conjecture by demonstrating finer grained dynamics at exponentially long time scales.”
• Circuit complexity in interacting QFTs and RG flows (2018, background): “Two interesting proposals were given in the context of AdS/CFT [27–32].”
• Circuit complexity for free fermions (2018, methodology): “olographic theories. The complexity=volume (CV) conjecture suggests that complexity is dual to the volume of an extremal (codimensionone) bulk surface anchored to a certain time slice in the boundary [1,4]. Alternatively, the complexity=action (CA) conjecture identies the complexity with the gravita”
• Liouville action as path-integral complexity: from continuous tensor networks to AdS/CFT (2017, background): “on some spacelike slice, say Σ, of the boundary, was first proposed in [21, 22] to be identified with the volume of a maximal volume space-like slice, say MΣ, in the bulk where the”
• On volumes of subregions in holography and complexity (2016, background): “In the following we briefly review the concept of quantum complexity, and its proposed holographic conjectures as given in [24–31].”
• Linear growth of quantum circuit complexity (2021, methodology): “are equivalent: (1) operating on the input qubits with P before the extended block”
• Addendum to computational complexity and black hole horizons (2014, methodology): “The argument illustrated in figure 1 of [1] shows that for large tW the complexity of 1.”
• Complexity and Shock Wave Geometries (2014, methodology): “This is precisely the behavior one would expect based on a quantum circuit model of complexity [18][8]: the rate of computation measured in gates per unit time is proportional to the product ST.”
• Chaos and complexity by design (2016, background): “[72] L. Susskind, “Computational Complexity and Black Hole Horizons,” Fortsch.”
• Measurement-Induced Phase Transitions in the Dynamics of Entanglement (2018, background): “[84] Leonard Susskind.”
• Complexity, action, and black holes (2015, background): “The complexity of the plasma dual to the black hole is also expected to increase long after local thermal equilibrium is reached, so it was proposed that the two growths are dual descriptions of the same phenomenon [4,5].”
• Holographic Complexity Equals Bulk Action? (2015, background): “One of the few holographic ideas about the black hole interior is that its growth is dual to the growth of quantum complexity [1, 2].”
• Many-Body Quantum Magic (2020, background): “[76] Leonard Susskind, “Computational Complexity and Black Hole Horizons,” arXiv e-prints , arXiv:1402.”
• Chaos, complexity, and random matrices (2017, background): “In the past few years, quantum complexity has been considered in holography as a possible CFT observable20 to study the late-time dynamics of the AdS black holes [50, 51].”
• Divergences in holographic complexity (2016, background): “2 Review of CV and CA In the CV conjecture of [1], the complexity C of the state |Ψ〉 of a holographic field theory on some spatial slice Σ on the boundary of an asymptotically AdS spacetime is identified with the volume V of the maximal volume codimension one slice B in the bulk having its boundary ”
• Complexity and entanglement for thermofield double states (2018, background): “The left and right sides of the geometry associated with the black hole dual to the TFD state are connected by a wormhole, or Einstein-Rosen bridge (ERB), whose volume increases for a time which is exponential in the number of degrees of freedom of the boundary theory [12,13].”