Complexity, action, and black holes

Brown, Adam R.; Roberts, Daniel A.; Susskind, Leonard; Swingle, Brian; Zhao, Ying

doi:10.1103/physrevd.93.086006

Cited by 619 publications

(1,330 citation statements)

References 63 publications

(147 reference statements)

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“…It was also shown in [5,6] that for the Einstein-Hilbert action, AdS black holes saturate the bound (1.1).…”

Section: Jhep01(2018)127mentioning

confidence: 99%

“…On this spacetime one can define the Wheeler-DeWitt patch, shown in figure 1. The patch is anchored at boundary times t L and t R , and the proposal of [5,6] equates the complexity of the thermofield dual state |ψ(t L , t r ) with the action evaluated on the Wheeler-DeWitt patch S WdW :…”

Section: Jhep01(2018)127mentioning

confidence: 99%

“…(For related work, including a few lecture notes, see [7]- [59].) The proposal of [5,6], which we refer to as Complexity-Action (CA) proposal, makes use of the holographic representation of the thermofield double state in a strongly coupled quantum field theory in terms of the eternal 1 We will consider the case of two-gates, but one can easily generalize the discussion to the k-gates.…”

Section: Introductionmentioning

confidence: 99%

“…where M is the mass of the system (check references [2]- [5] for some violations of this bound). Recently a holographic recipe has been proposed [5,6] to compute complexity for thermofield double states in strongly coupled quantum field theories.…”

Section: Introductionmentioning

confidence: 99%

“…Recently a holographic recipe has been proposed [5,6] to compute complexity for thermofield double states in strongly coupled quantum field theories. (For related work, including a few lecture notes, see [7]- [59].)…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

On complexity of holographic flavors

Abad

Kulaxizi

Parnachev

2018

J. High Energ. Phys.

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Quantum complexity of a thermofield double state in a strongly coupled quantum field theory has been argued to be holographically related to the action evaluated on the Wheeler-DeWitt patch. The growth rate of quantum complexity in systems dual to Einstein-Hilbert gravity saturates a bound which follows from the Heisenberg uncertainty principle. We consider corrections to the growth rate in models with flavor degrees of freedom. They are realized by adding a small number of flavor branes to the system. Holographically, such corrections come from the DBI action of the flavor branes evaluated on the Wheeler-DeWitt patch. We relate corrections to the growth of quantum complexity to corrections to the mass of the system, and observe that the bound on the growth rate is never violated.

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“…It was also shown in [5,6] that for the Einstein-Hilbert action, AdS black holes saturate the bound (1.1).…”

Section: Jhep01(2018)127mentioning

confidence: 99%

Section: Jhep01(2018)127mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

On complexity of holographic flavors

Abad

Kulaxizi

Parnachev

2018

J. High Energ. Phys.

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Universality of black hole quantum computing

Dvali

Gómez

Lüst

et al. 2016

Fortschritte der Physik

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By analyzing the key properties of black holes from the point of view of quantum information, we derive a model-independent picture of black hole quantum computing. It has been noticed that this picture exhibits striking similarities with quantum critical condensates, allowing the use of a common language to describe quantum computing in both systems. We analyze such quantum computing by allowing coupling to external modes, under the condition that the external influence must be soft-enough in order not to offset the basic properties of the system. We derive modelindependent bounds on some crucial time-scales, such as the times of gate operation, decoherence, maximal entanglement and total scrambling. We show that for black hole type quantum computers all these time-scales are of the order of the black hole half-life time. Furthermore, we construct explicitly a set of Hamiltonians that generates a universal set of quantum gates for the black hole type computer. We find that the gates work at maximal energy efficiency. Furthermore, we establish a fundamental bound on the complexity of quantum circuits encoded on these systems, and characterize the unitary operations that are implementable. It becomes apparent that the computational power is very limited due to the fact that the black hole life-time is of the same order of the gate operation time. As a consequence, it is impossible to retrieve its information, within the life-time of a black hole, by externally coupling to the black hole qubits. However, we show that, in principle, coupling to some of the internal degrees of freedom allows acquiring knowledge about the micro-state. Still, due to the trivial complexity of operations that can be performed, there is no time advantage over the collection of Hawking radiation and subsequent decoding.

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Circuit Complexity in Topological Quantum Field Theory

Couch

Fan²,

Shashi

2022

Fortschritte der Physik

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Quantum circuit complexity has played a central role in recent advances in holography and many‐body physics. Within quantum field theory, it has typically been studied in a Lorentzian (real‐time) framework. In a departure from standard treatments, we aim to quantify the complexity of the Euclidean path integral. In this setting, there is no clear separation between space and time, and the notion of unitary evolution on a fixed Hilbert space no longer applies. As a proof of concept, we argue that the pants decomposition provides a natural notion of circuit complexity within the category of 2‐dimensional bordisms and use it to formulate the circuit complexity of states and operators in 2‐dimensional topological quantum field theory. We comment on analogies between our formalism and others in quantum mechanics, such as tensor networks and second quantization.

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Complexity, action, and black holes

Cited by 619 publications

References 63 publications

On complexity of holographic flavors

On complexity of holographic flavors

Universality of black hole quantum computing

Circuit Complexity in Topological Quantum Field Theory

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