Quantum Gravity in the Lab. I. Teleportation by Size and Traversable Wormholes

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Quantum Gravity in the Lab. I. Teleportation by Size and Traversable Wormholes

Adam R. Brown, Hrant Gharibyan, Stefan Leichenauer, Henry W. Lin, Sepehr Nezami, Grant Salton, Leonard Susskind, Brian Swingle, and Michael Walter

PRX Quantum 4, 010320 – Published 27 February 2023

Abstract

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 Gao et al. [J. High Energy Phys., 2017, 151 (2017)] and Maldacena et al. [Fortschr. Phys., 65, 1700034 (2017)]: 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 semiclassical holographic wormhole corresponds to a rather special property of the operator-size distribution that 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 signaling 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 that are feasible with current technology in two experimental platforms: Rydberg-atom arrays and trapped ions.

Received 29 September 2021
Revised 2 November 2022
Accepted 23 December 2022
Corrected 18 May 2023

DOI:https://doi.org/10.1103/PRXQuantum.4.010320

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Quantum algorithms Quantum entanglement Quantum gravity Quantum teleportation

Quantum Information, Science & TechnologyGravitation, Cosmology & AstrophysicsParticles & Fields

Corrections

18 May 2023

Correction: The fifth affiliation was a duplicate of the third affiliation and was removed. This change necessitated renumbering of the remaining affiliation indicators.

Authors & Affiliations

Adam R. Brown^1,2, Hrant Gharibyan ^2,3,*, Stefan Leichenauer¹, Henry W. Lin^1,4, Sepehr Nezami^1,2,3, Grant Salton ^2,3,5,6, Leonard Susskind^1,2, Brian Swingle⁷, and Michael Walter^8,9

¹Google, Mountain View, California 94043, USA
²Department of Physics, Stanford University, Stanford, California 94305, USA
³Institute for Quantum Information and Matter, Caltech, Pasadena, California 91125, USA
⁴Physics Department, Princeton University, Princeton, New Jersey 08540, USA
⁵Amazon Quantum Solutions Lab, Seattle, Washington 98170, USA
⁶Amazon Web Services (AWS) Center for Quantum Computing, Pasadena, California 91125, USA
⁷Condensed Matter Theory Center, Joint Center for Quantum Information and Computer Science, Maryland Center for Fundamental Physics, and Department of Physics, University of Maryland, College Park, Maryland 20742, USA
⁸Faculty of Computer Science, Ruhr University Bochum, D-44801 Bochum, Germany
⁹Korteweg–de Vries Institute for Mathematics, Institute for Theoretical Physics, Institute for Logic, Language and Computation & QuSoft, University of Amsterdam, 1090 GE Amsterdam, Kingdom of the Netherlands

^*hrant@caltech.edu

Popular Summary

The construction of a unified theory of quantum gravity has been one of the most intensely studied open problems in theoretical physics since the 1950s, with most ideas stemming from theoretical aspects of quantum field theory, general relativity, string theory, and loop quantum gravity. A leading candidate for such a theory is the so-called anti–de Sitter – conformal field theory (AdS-CFT) correspondence, which is a holographic theory of quantum gravity.

In this paper, we first identify a common phenomenon of chaotic quantum systems and then we use this new phenomenon to propose a class of experiments that can probe the relationship between quantum physics and holographic theories of gravity. Specifically, we describe a holographic teleportation protocol that can be readily executed in table-top experiments in near-term quantum devices. In terms of the bulk perspective in AdS-CFT, this protocol is dual to the motion of a particle traveling through a traversable wormhole connecting two disconnected space-time regions. From the boundary perspective, quantum information is first scrambled, then two different boundaries are coupled together, and then the information is unscrambled. This unscrambling process happens automatically, leading to a new type of quantum teleportation protocol that we call teleportation by size.

We argue that the transmission of a signal through a semiclassical holographic wormhole corresponds to a rather special property of the operator-size distribution that we call size winding. We also show that the protocol works beyond models that exhibit size-winding dynamics; however, in this case one may not be able to ascribe a gravitational interpretation to the phenomenon. Lastly, we outline experimentally feasible implementations of our protocol using current technology in two experimental platforms: Rydberg-atom arrays and trapped ions.

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Quantum Gravity in the Lab. II. Teleportation by Size and Traversable Wormholes

Sepehr Nezami, Henry W. Lin, Adam R. Brown, Hrant Gharibyan, Stefan Leichenauer, Grant Salton, Leonard Susskind, Brian Swingle, and Michael Walter

PRX Quantum 4, 010321 (2023)

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Vol. 4, Iss. 1 — February - April 2023

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Images

Figure 1
The circuits considered in this paper, with $H_{L} = H_{R}^{T}$ . Downward arrows indicate acting with the inverse of the time-evolution operator. In both protocols, the goal is to transmit information from the left to the right. (a) The state-transfer protocol calls for us to discard the left message qubits ( $A_{L}$ ) and replace them with our message $Ψ_{in}$ . The output state on the right then defines a channel applied to the input state. (b) The operator-transfer protocol calls for the operator $O$ to be applied to $A_{L}$ . Based on the choice of operator, the output state on the right is modified, similar to a perturbation-response experiment.
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Figure 2
The Penrose diagram of wormholes. Left: without the coupling, a message or particle inserted at early times on the left passes through the left horizon and hits the singularity (the top line of the diagram). Right: in the presence of the left-right coupling, the message hits the negative-energy shock wave (the thick blue line) created by the coupling. The effect of the collision is to rescue the message from behind the right horizon.
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Figure 3
(a) An Infinite-temperature holographic teleportation circuit, with $U = e^{- i H t}$ . (b) An equivalent circuit to (a) after circuit manipulations. (c) The result of replacing the trace by projecting the carrier qubits onto $| ϕ^{+} ⟩$ . When the teleportation has high fidelity, this projection has a negligible effect on the final state. For many systems of interest, the operator $\tilde{S}$ enclosed in the dashed rectangle approximately implements the unitary defined in Eq. (2) for some appropriate $g^{'}$ .
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Figure 4
A short summary of teleportation by size, discussing different systems, different patterns of operator growth, and the consequence of each growth pattern for signal transmission. (a) Operator growth, late time, most quantum systems: teleports one qubit through state-transfer mechanism; sgn( $g$ ) independent; infinite temperature. (b) Operator growth, intermediate time: chaotic spin chains, random circuits; teleports many qubits through state-transfer mechanism; sgn( $g$ ) independent; infinite temperature. (c) Size winding (damped), low temperature: teleports through state-transfer mechanism; weak sgn( $g$ ) dependence; works weakly for “operator transfer.” (d) Perfect size winding (not damped), low temperature: could teleport through state-transfer mechanism; strong sgn( $g$ ) dependence but limited fidelity; works perfectly for “operator transfer” slightly before scrambling time; strong signature of a geometrical wormhole. Blue, initial operator-size distribution; red, winding size distribution of the time-evolved operator.
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Figure 5
The expectation value of $Z_{1 R}$ after injection of a $Z_{1 L} = 1$ state on the left system. The black dots are direct numerical simulation of the protocol in the quantum kicked Ising model with $n = 7$ spins on the left and right and with $J = b = π / 4$ and $h_{i}$ drawn from a box distribution of width $0.5$ . Left: the signal at fixed large time as a function of $g$ . The black circles are the exact numerical simulation. The red curve is the theory prediction in Eq. (20). Right: the signal at fixed $g$ as a function of the time step. The black circles are the exact numerical simulation. The red curve is a crude approximation where we assume that Eq. (20) holds at all times, with the effective system size replaced as $n \to min (t + 1, n)$ .
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