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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Approximate Quantum Codes From Long Wormholes

We discuss families of approximate quantum error correcting codes which arise as the nearly-degenerate ground states of certain quantum many-body Hamiltonians composed of non-commuting terms. For exact codes, the conditions for error correction can be formulated in terms of the vanishing of a two-sided mutual information in a low-temperature thermofield double state. We consider a notion of distance for approximate codes obtained by demanding that this mutual information instead be small, and we evaluate this mutual information for the SYK model and for a family of low-rank SYK models. After an extrapolation to nearly zero temperature, we find that both kinds of models produce fermionic codes with constant rate as the number, N , of fermions goes to infinity. For SYK, the distance scales as N 1 / 2 , and for low-rank SYK, the distance can be arbitrarily close to linear scaling, e.g. N .99 , while maintaining a constant rate. We also consider an analog of the no low-energy trivial states property which we dub the no low-energy adiabatically accessible states property and show that these models do have low-energy states that can be prepared adiabatically in a time that does not scale with system size N . We discuss a holographic model of these codes in which the large code distance is a consequence of the emergence of a long wormhole geometry in a simple model of quantum gravity.

Physics↗
NASA NTRS1989

Conformal scalar field wormholes

The Euclidian Einstein equations with a cosmological constant and a conformally coupled scalar field are solved, taking the metric to be of the Robertson-Walker type. In the case Lambda = 0, solutions are found which represent a wormhole connecting two asymptotically flat Euclidian regions. In the case Lambda greater than 0, the solutions represent tunneling from a small Tolman-like universe to a large Robertson-Walker universe.

Halliwell, Jonathan J.↗
DOE OSTI2024

The lion, the witch, and the wormhole: ensemble averaging the symmetric product orbifold

Abstract We consider the ensemble average of two dimensional symmetric product orbifold CFTs Sym N (𝕋 D ) over the Narain moduli space. We argue for a bulk dual given byNcopies of an abelian Chern-Simons theory coupled to topological gravity, endowed with a discrete gauge symmetry exchanging theNcopies. As a check of this proposal, we calculate the ensemble average of various partition and correlation functions of the symmetric product orbifold theory and compare the resulting expressions to gauge theory quantities in the bulk. We comment on the ensemble average of the tensionless string partition function on AdS 3 × S 3 × 𝕋 4 by considering the specific case ofD= 4 with the addition of supersymmetry.

Physics↗
DOE OSTI2023

Wormhole teleportation

Talk presented Sept 4, 2023 at the Wilhelm and Else Heraeus Seminar on Simulations of Quantum Field Theories, Oberwolz, Austria. Slides contain information previously published in Nature 612, pages 51–55 (2022), and arXiv:2303.15423

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Comment on "Comment on "Traversable wormhole dynamics on a quantum processor" "

We observe that the comment of [1, arXiv:2302.07897] is consistent with [2] on key points: i) the microscopic mechanism of the experimentally observed teleportation is size winding and ii) the system thermalizes and scrambles at the time of teleportation. These properties are consistent with a gravitational interpretation of the teleportation dynamics, as opposed to the late-time dynamics. The objections of [1] concern counterfactual scenarios outside of the experimentally implemented protocol.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

A precision test of averaging in AdS/CFT

We reconsider the role of wormholes in the AdS/CFT correspondence. We focus on Euclidean wormholes that connect two asymptotically AdS or hyperbolic regions with $\mathbb{S}$ 1 × $\mathbb{S}$ d-1 boundary. There is no solution to Einstein’s equations of this sort, as the wormholes possess a modulus that runs to infinity. To find on-shell wormholes we must stabilize this modulus, which we can do by fixing the total energy on the two boundaries. Such a wormhole gives the saddle point approximation to a non-standard problem in quantum gravity, where we fix two asymptotic boundaries and constrain the common energy. Crucially the dual quantity does not factorize even when the bulk is dual to a single CFT, on account of the fixed energy constraint. From this quantity we extract a smeared version of the microcanonical spectral form factor. For a chaotic theory this quantity is self-averaging, i.e. well-approximated by averaging over energy windows, or over coupling constants. We go on to give a precision test involving the microcanonical spectral form factor where the two replicas have slightly different coupling constants. In chaotic theories this form factor is known to smoothly decay at a rate universally predicted in terms of one replica physics, provided that there is an average either over a window or over couplings. We compute the expected decay rate for holographic theories, and the form factor from a wormhole, and the two exactly agree for a wide range of two-derivative effective field theories in AdS. This gives a precision test of averaging in AdS/CFT. Our results interpret a number of confusing facts about wormholes and factorization in AdS and suggest that we should regard gravitational effective field theory as a mesoscopic description, analogous to semiclassical mesoscopic descriptions of quantum chaotic systems.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Entanglement between two gravitating universes

Abstract We study two disjoint universes in an entangled pure state. When only one universe contains gravity, the path integral for the n th Rényi entropy includes a wormhole between the n copies of the gravitating universe, leading to a standard ‘island formula’ for entanglement entropy consistent with unitarity of quantum information. When both universes contain gravity, gravitational corrections to this configuration lead to a violation of unitarity. However, the path integral is now dominated by a novel wormhole with 2 n boundaries connecting replica copies of both universes. The analytic continuation of this contribution involves a quotient by Z n replica symmetry, giving a cylinder connecting the two universes. When entanglement is large, this configuration has an effective description as a ‘swap wormhole’, a geometry in which the boundaries of the two universes are glued together by a ‘swaperator’. This description allows precise computation of a generalized entropy-like formula for entanglement entropy. The quantum extremal surface computing the entropy lives on the Lorentzian continuation of the cylinder/swap wormhole, which has a connected Cauchy slice stretching between the universes—a realization of the ER = EPR idea. The new wormhole restores unitarity of quantum information.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Firewalls at exponentially late times

We consider a version of the typical state firewall setup recently reintroduced by Stanford and Yang, who found that wormholes may create firewalls. We examine a late-time scaling limit in JT gravity in which one can resum the expansion in the number of wormholes, and we use this to study the exact distribution of interior slices at times exponential in the entropy. We consider a thermofield double with and without early perturbations on a boundary. These perturbations can appear on interior slices as dangerous high energy shockwaves. For exponentially late times, wormholes tend to teleport the particles created by perturbations and render the interior more dangerous. In states with many perturbations separated by large times, the probability of a safe interior is exponentially small, even though these would be safe without wormholes. With perturbation, even in the safest state we conceive, the odds of encountering a shock are fifty-fifty. One interpretation of the phenomenon is that wormholes can change time-ordered contours into effective out-of-time-ordered folds, making shockwaves appear in unexpected places.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Black hole complementarity and ER/EPR

In this paper, we demonstrate that wormholes must be entangled regardless of asymptotic boundary conditions. By assuming black hole complementarity, we argue that traversable wormholes instantiate entanglement-assisted quantum channels and that this entanglement must be present between the stretched horizons as an initial condition prior to traversability. In conclusion, this result demonstrates the forward direction of the ER/EPR conjectures.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

General bounds on holographic complexity

We prove a positive volume theorem for asymptotically AdS spacetimes: the maximal volume slice has nonnegative vacuum-subtracted volume, and the vacuum-subtracted volume vanishes if and only if the spacetime is identically pure AdS. Under the Complexity=Volume proposal, this constitutes a positive holographic complexity theorem. The result features a number of parallels with the positive energy theorem, including the assumption of an energy condition that excludes false vacuum decay (the AdS weak energy condition). Our proof is rigorously established in broad generality in four bulk dimensions, and we provide strong evidence in favor of a generalization to arbitrary dimensions. Our techniques also yield a holographic proof of Lloyd’s bound for a class of bulk spacetimes. We further establish a partial rigidity result for wormholes: wormholes with a given throat size are more complex than AdS-Schwarzschild with the same throat size.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗