arXiv subjects

Leonard Susskind

Publications and source records attributed to Leonard Susskind.

At least 37 records · Page 2Linked to original sources

arXiv2021

Entanglement and Chaos in De Sitter Holography: An SYK Example

Entanglement, chaos, and complexity are as important for de Sitter space as for AdS and for black holes. There are similarities and great differences between AdS and dS in how these concepts are manifested in the space-time geometry. In the first part of this paper the Ryu-Takayanagi prescription, the theory of fast scrambling, and the holographic complexity correspondence are reformulated for de Sitter space. Criteria are proposed for a holographic model to describe de Sitter space. The criteria can be summarized by the requirement that scrambling and complexity growth must be "hyperfast." In the later part of the paper I show that a certain limit of SYK is a concrete, computable, holographic model of de Sitter space. Calculations are described which support the conjecture.

hep-th↗

arXiv2021

Black Hole-String Correspondence

I was asked to give a brief review of the black hole-string correspondence as a warm-up for a longer SITP-group discussion of a recent paper by Chen, Maldacena, and Witten. Here are my notes in written form.

hep-th↗

arXiv2021

Black Holes Hint Towards De Sitter-Matrix Theory

De Sitter black holes and other non-perturbative configurations can be used to probe the holographic degrees of freedom of de Sitter space. For small black holes evidence was first given in seminal work of Banks, Fiol, and Morrise; and followups by Banks and Fischler; showing that dS is described by a form of matrix theory. For large black holes the evidence given here is new: Gravitational calculations and matrix theory calculations of the rates of exponentially rare fluctuations match one another in surprising detail. The occurrence of the Nariai geometry and the "inside-out" transition are especially interesting examples which I explain.

hep-th↗

arXiv2021

Three Impossible Theories

I will begin by conjecturing a cosmological generalization of black hole complementarity (also known as the central dogma). I will then discuss three theories and argue that they are inconsistent with second law of thermodynamics if the cosmological version of the dogma is correct. The three theories are: the big rip; cyclic cosmology; and the Farhi-Guth-Guven mechanism for creating inflating universes behind black hole horizons.

hep-th↗

arXiv2021

De Sitter Holography: Fluctuations, Anomalous Symmetry, and Wormholes

The Goheer-Kleban-Susskind no-go theorem says that the symmetry of de Sitter space is incompatible with finite entropy. The meaning and consequences of the theorem are discussed in the light of recent developments in holography and gravitational path integrals. The relation between the GKS theorem, Boltzmann fluctuations, wormholes, and exponentially suppressed non-perturbative phenomena suggests: the classical symmetry between different static patches is broken; and that eternal de Sitter space -- if it exists at all -- is an ensemble average.

hep-th↗

arXiv2021

The Complexity Geometry of a Single Qubit

The computational complexity of a quantum state quantifies how hard it is to make. `Complexity geometry', first proposed by Nielsen, is an approach to defining computational complexity using the tools of differential geometry. Here we demonstrate many of the attractive features of complexity geometry using the example of a single qubit, which turns out to be rich enough to be illustrative but simple enough to be illuminating.

hep-th↗

arXiv2021

Quantum Gravity in the Lab: Teleportation by Size and Traversable Wormholes

With the long-term goal of studying models of quantum gravity in the lab, we propose holographic teleportation protocols that can be readily executed in table-top experiments. These protocols exhibit similar behavior to that seen in the recent traversable wormhole constructions of [1,2]: information that is scrambled into one half of an entangled system will, following a weak coupling between the two halves, unscramble into the other half. We introduce the concept of teleportation by size to capture how the physics of operator-size growth naturally leads to information transmission. The transmission of a signal through a semi-classical holographic wormhole corresponds to a rather special property of the operator-size distribution we call size winding. For more general systems (which may not have a clean emergent geometry), we argue that imperfect size winding is a generalization of the traversable wormhole phenomenon. In addition, a form of signalling continues to function at high temperature and at large times for generic chaotic systems, even though it does not correspond to a signal going through a geometrical wormhole, but rather to an interference effect involving macroscopically different emergent geometries. Finally, we outline implementations feasible with current technology in two experimental platforms: Rydberg atom arrays and trapped ions.

quant-ph↗

arXiv2021

Quantum Gravity in the Lab: Teleportation by Size and Traversable Wormholes, Part II

In [1] we discussed how quantum gravity may be simulated using quantum devices and gave a specific proposal -- teleportation by size and the phenomenon of size-winding. Here we elaborate on what it means to do 'Quantum Gravity in the Lab' and how size-winding connects to bulk gravitational physics and traversable wormholes. Perfect size-winding is a remarkable, fine-grained property of the size wavefunction of an operator; we show from a bulk calculation that this property must hold for quantum systems with a nearly-AdS_2 bulk. We then examine in detail teleportation by size in three systems: the Sachdev-Ye-Kitaev model, random matrices, and spin chains, and discuss prospects for realizing these phenomena in near-term quantum devices.

quant-ph↗

arXiv2021

Electric Forces in the Charged SYK Model

The connection between gravitational force and operator growth, reported in earlier papers, is generalized to include electromagnetic forces. It is shown how in the U(1)-invariant SYK system electric forces emerge through the same mechanisms -- the momentum-size correspondence, and operator growth -- that give rise to gravitational force. The unit of electric charge implied by the U(1)-SYK theory is consistent with a Kaluza-Klein radius inverse to the characteristic energy scale of the SYK theory.

hep-th↗

arXiv2020

On the Hardness of Detecting Macroscopic Superpositions

When is decoherence "effectively irreversible"? Here we examine this central question of quantum foundations using the tools of quantum computational complexity. We prove that, if one had a quantum circuit to determine if a system was in an equal superposition of two orthogonal states (for example, the $|$Alive$\rangle$ and $|$Dead$\rangle$ states of Schrödinger's cat), then with only a slightly larger circuit, one could also $\mathit{swap}$ the two states (e.g., bring a dead cat back to life). In other words, observing interference between the $|$Alive$\rangle$and $|$Dead$\rangle$ states is a "necromancy-hard" problem, technologically infeasible in any world where death is permanent. As for the converse statement (i.e., ability to swap implies ability to detect interference), we show that it holds modulo a single exception, involving unitaries that (for example) map $|$Alive$\rangle$ to $|$Dead$\rangle$ but $|$Dead$\rangle$ to -$|$Alive$\rangle$. We also show that these statements are robust---i.e., even a $\mathit{partial}$ ability to observe interference implies partial swapping ability, and vice versa. Finally, without relying on any unproved complexity conjectures, we show that all of these results are quantitatively tight. Our results have possible implications for the state dependence of observables in quantum gravity, the subject that originally motivated this study.

quant-ph↗

arXiv2020

A Sparse Model of Quantum Holography

We study a sparse version of the Sachdev-Ye-Kitaev (SYK) model defined on random hypergraphs constructed either by a random pruning procedure or by randomly sampling regular hypergraphs. The resulting model has a new parameter, $k$, defined as the ratio of the number of terms in the Hamiltonian to the number of degrees of freedom, with the sparse limit corresponding to the thermodynamic limit at fixed $k$. We argue that this sparse SYK model recovers the interesting global physics of ordinary SYK even when $k$ is of order unity. In particular, at low temperature the model exhibits a gravitational sector which is maximally chaotic. Our argument proceeds by constructing a path integral for the sparse model which reproduces the conventional SYK path integral plus gapped fluctuations. The sparsity of the model permits larger scale numerical calculations than previously possible, the results of which are consistent with the path integral analysis. Additionally, we show that the sparsity of the model considerably reduces the cost of quantum simulation algorithms. This makes the sparse SYK model the most efficient currently known route to simulate a holographic model of quantum gravity. We also define and study a sparse supersymmetric SYK model, with similar conclusions to the non-supersymmetric case. Looking forward, we argue that the class of models considered here constitute an interesting and relatively unexplored sparse frontier in quantum many-body physics.

cond-mat.str-el↗

arXiv2020

Complexity and Momentum

Previous work has explored the connections between three concepts -- operator size, complexity, and the bulk radial momentum of an infalling object -- in the context of JT gravity and the SYK model. In this paper we investigate the higher dimensional generalizations of these connections. We use a toy model to study the growth of an operator when perturbing the vacuum of a CFT. From circuit analysis we relate the operator growth to the rate of increase of complexity and check it by complexity-volume duality. We further give an empirical formula relating complexity and the bulk radial momentum that works from the time that the perturbation just comes in from the cutoff boundary, to after the scrambling time.

hep-th↗

arXiv2020

Black Holes at Exp-time

Classical GR governs the evolution of black holes for a long time, but at some exponentially large time it must break down. The breakdown, and what comes after it, is not well understood. In this paper I'll discuss the problem using concepts drawn from complexity geometry. In particular the geometric concept of cut locus plays a key role.

hep-th↗

arXiv2020

Horizons Protect Church-Turing

The quantum-Extended Church-Turing thesis is a principle of physics as well as computer science. It asserts that the laws of physics will prevent the construction of a machine that can efficiently determine the results of any calculation which cannot be done efficiently by a quantum Turing machine (or a universal quantum circuit). In this note I will argue that an observer falling into a black hole can learn the result of such a calculation in a very short time, thereby seemingly violating the thesis. A viable reformulation requires that the thesis only applies to observers who have access to the holographic boundary of space. The properties of the horizon play a crucial a role in protecting the thesis. The arguments are closely related to, and were partially motivated by a recent paper by Bouland, Fefferman, and Vazirani, and by a question raised by Aaronson.

hep-th↗

arXiv2019

The Python's Lunch: geometric obstructions to decoding Hawking radiation

According to Harlow and Hayden [arXiv:1301.4504] the task of distilling information out of Hawking radiation appears to be computationally hard despite the fact that the quantum state of the black hole and its radiation is relatively un-complex. We trace this computational difficulty to a geometric obstruction in the Einstein-Rosen bridge connecting the black hole and its radiation. Inspired by tensor network models, we conjecture a precise formula relating the computational hardness of distilling information to geometric properties of the wormhole - specifically to the exponential of the difference in generalized entropies between the two non-minimal quantum extremal surfaces that constitute the obstruction. Due to its shape, we call this obstruction the "Python's Lunch", in analogy to the reptile's postprandial bulge.

hep-th↗

arXiv2019

Complexity Geometry and Schwarzian Dynamics

A celebrated feature of SYK-like models is that at low energies, their dynamics reduces to that of a single variable. In many setups, this "Schwarzian" variable can be interpreted as the extremal volume of the dual black hole, and the resulting dynamics is simply that of a 1D Newtonian particle in an exponential potential. On the complexity side, geodesics on a simplified version of Nielsen's complexity geometry also behave like a 1D particle in a potential given by the angular momentum barrier. The agreement between the effective actions of volume and complexity succinctly summarizes various strands of evidence that complexity is closely related to the dynamics of black holes.

hep-th↗

arXiv2019

Electromagnetic Memory

An elementary derivation of the electromagnetic memory effect is given. An experimental setup to detect it is suggested.

hep-th↗

arXiv2019

Complexity and Newton's Laws

In a recent note I argued that the holographic origin of gravitational attraction is the quantum mechanical tendency for operators to grow under time evolution. In a followup the claim was tested in the context of the SYK theory and its bulk dual---the theory of near-extremal black holes. In this paper I give an improved version of the size-momentum correspondence and show that Newton's laws of motion are a consequence. Operator size is closely related to complexity. Therefore one may say that gravitational attraction is a manifestation of the tendency for complexity to increase. The improved version of the size-momentum correspondence can be justified by the arguments of Lin, Maldacena, and Zhao constructing symmetry generators for the approximate symmetries of the SYK model.

hep-th↗