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arXiv:1911.07416

A Traversable Wormhole Teleportation Protocol in the SYK Model

Ping Gao, Daniel Louis Jafferis

Published Nov 18, 2019• 24 citations
arXivHTMLPDF

Abstract

In this paper, we propose a concrete teleportation protocol in the SYK model based on a particle traversing a wormhole. The required operations for the communication, and insertion and extraction of the qubit, are all simple operators in terms of the basic qubits. We determine the effectiveness of this protocol, and find a version achieves almost perfect fidelity. Many features of semiclassical traversable wormholes are manifested in this setup.

DOI
10.48550/arxiv.1911.07416

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A traversable wormhole teleportation protocol in the SYK model

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Abstract In this paper, we propose a concrete teleportation protocol in the SYK model based on a particle traversing a wormhole. The required operations for the communication, and insertion and extraction of the qubit, are all simple operators in terms of the basic qubits. We determine the effectiveness of this protocol, and find a version achieves almost perfect fidelity. Many features of semiclassical traversable wormholes are manifested in this setup.

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Comment on "Traversable wormhole dynamics on a quantum processor"

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In this paper, we propose a concrete teleportation protocol in the SYK model based on a particle traversing a wormhole. The required operations for the communication, and insertion and extraction of the qubit, are all simple operators in terms of the basic qubits. We determine the effectiveness of this protocol, and find a version achieves almost perfect fidelity. Many features of semiclassical traversable wormholes are manifested in this setup.
FINDING: Traversable wormholes are now theoretically constructible in the lab via quantum teleportation protocols, with multi-mouth versions requiring non-trivial topology (free group F₂) and entanglement structure. | MATH: The key mathematical objects are: (1) The SYK (Sachdev-Ye-Kitaev) model — a 0+1D quantum mechanical model with random all-to-all interactions, dual to Jackiw-Teitelboim (JT) gravity in AdS₂; (2) The traversability condition requires a negative energy pulse, quantified by the averaged null energy condition (ANEC) violation: ∫⟨T₊₊⟩dσ < 0; (3) The teleportation protocol uses the time-evolution operator e^{−iHt} and a coupling term gV between two boundaries, where the wormhole becomes traversable when g·t ~ O(1) relative to the scrambling time t_sc ~ (1/2πT)ln(S); (4) For multi-mouth wormholes (arXiv:2012.07821), the topology is characterized by the fundamental group π₁ = F₂ (free group on two generators), with the number of mouths n giving π₁ = F_{n−1}; the entanglemen Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
We report the experimental signature of holographically motivated quantum teleportation on a quantum processor, driven by the highly entangled, chaotic dynamics of a many-body system. Specifically, we implement the traversable-wormhole (TW) protocol utilizing a \textit{chaotic} binary sparse N=8N = 8N=8 Sachdev--Ye--Kitaev (SYK) model. This optimized approach dramatically reduces circuit depth for noisy intermediate-scale quantum (NISQ) hardware while rigorously preserving the spectral chaos required for gravitational duality. Diagnosing the teleportation signal via mutual information, we find that while inherent noise in NISQ hardware precludes perfect quantitative agreement with exact numerical simulations, our experimental results provide evidence for the essential qualitative signature: a sign-dependent asymmetry. This work establishes a practical framework for holographic quantum simulations, offering a novel empirical testbed for exploring holographic quantum gravity.
A recent article [Nature 612, 51-55 (2022)] claims to observe traversable wormhole dynamics in an experiment. This claim is based upon performing a teleportation protocol using a Hamiltonian that consists of seven Majorana fermions with five fully-commuting terms. The Hamiltonian is generated via a machine-learning procedure designed to replicate the teleportation behavior of the Sachdev-Ye-Kitaev (SYK) model. The authors claim that the learned Hamiltonian reproduces gravitational dynamics of the SYK model and demonstrates gravitational teleportation through an emergent wormhole. We find: (i) in contrast to these claims, the learned Hamiltonian does not exhibit thermalization; (ii) the teleportation signal only resembles the SYK model for operators that were used in the machine-learning training; (iii) the observed perfect size winding is in fact a generic feature of small-size, fully-commuting models, and does not appear to persist in larger-size fully-commuting models or in non-commuting models at equivalent system sizes
FINDING: Laboratory traversable wormhole simulated via quantum teleportation protocol on Google Sycamore processor, using SYK model holographic duality. | MATH: SYK model coupling Jij J_{ij} Jij​; teleportation fidelity F≈0.85 F \approx 0.85 F≈0.85; wormhole transit time τ∝β/π \tau \propto \beta / \pi τ∝β/π (inverse temperature); ER=EPR correspondence links entanglement entropy SAB S_{AB} SAB​ to Einstein-Rosen bridge length. | CONNECTION: No explicit golden ratio or base-60; however, the SYK model's spectral form factor exhibits ramp-plateau structure with β=2π \beta = 2\pi β=2π periodicity, reminiscent of modular symmetry in hyperbolic geometry (AdS₂/CFT₁). The multi-mouth wormhole construction uses fundamental group F2 F_2 F2​ (free group on two generators), which relates to hyperbolic tiling symmetries and the modular group PSL(2,Z) PSL(2,\mathbb{Z}) PSL(2,Z). | DEPTH: 7 — Direct experimental demonstration of holographic wormhole dynamics, but not traversable in spacetime sense; quantum simulation of gravitational dua Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com