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arXiv:2405.07876

Long-range wormhole teleportation

Joseph Lykken, Daniel Jafferis, Alexander Zlokapa, David K. Kolchmeyer, Samantha I. Davis, Hartmut Neven, Maria Spiropulu

Published May 13, 2024• 3 citations
arXivHTMLPDF

Abstract

We extend the protocol of Gao and Jafferis arXiv:1911.07416 to allow wormhole teleportation between two entangled copies of the Sachdev-Ye-Kitaev (SYK) model communicating only through a classical channel. We demonstrate in finite $N$ simulations that the protocol exhibits the characteristic holographic features of wormhole teleportation discussed and summarized in Jafferis et al. https://www.nature.com/articles/s41586-022-05424-3 . We review and exhibit in detail how these holographic features relate to size winding which, as first shown by Brown et al. arXiv:1911.06314 and Nezami et al. arXiv:2102.01064, encodes a dual description of wormhole teleportation.

DOI
10.7907/0b9qh-jt654

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We extend the protocol of Gao and Jafferis arXiv:1911.07416 to allow wormhole teleportation between two entangled copies of the Sachdev-Ye-Kitaev (SYK) model communicating only through a classical channel. We demonstrate in finite NNN simulations that the protocol exhibits the characteristic holographic features of wormhole teleportation discussed and summarized in Jafferis et al. https://www.nature.com/articles/s41586-022-05424-3 . We review and exhibit in detail how these holographic features relate to size winding which, as first shown by Brown et al. arXiv:1911.06314 and Nezami et al. arXiv:2102.01064, encodes a dual description of wormhole teleportation.
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
A bstract The rapid development of quantum science and technology is leading us into an era where quantum many-body systems can be comprehended through quantum simulations. Holographic duality, which states gravity and spacetime can emerge from strongly interacting systems, then offers a natural avenue for the experimental study of gravity physics without delving into experimentally infeasible high energies. A prominent example is the simulation of traversable wormholes through the wormhole teleportation protocol, attracting both theoretical and experimental attention. In this work, we develop the theoretical framework for computing the fidelity of wormhole teleportation in N -qubit systems with all-to-all interactions, quantified by mutual information and entanglement negativity. The main technique is the scramblon effective theory, which captures universal out-of-time-order correlations in generic chaotic systems. We clarify that strong couplings between the two systems are essential for simulating the probe limit of semi-classical traversable wormholes using strongly interacting systems with near-maximal chaos. However, the teleportation signal diminishes rapidly when reducing the system size N , requiring a large number of qubits to observe a sharp signature of emergent geometry by simulating the Sachdev-Ye-Kitaev model. This includes both the causal time-order of signals and the asymmetry of the teleportation signal for coupling with different signs. As a comparison, the teleportation signal increases when reducing N in weakly interacting systems. We also analyze the fidelity of the generalized encoding scheme in fermionic string operators.
In the Sachdev-Ye-Kitaev (SYK) model, traversable wormhole teleportation fidelity probes the many-body scrambling of holographic black holes. We apply a gravitational-wave-inspired periodic Floquet deformation derived from the lowest-dimensional bilinear SYK4\text{SYK}_4SYK4​ sector to the boundary, thereby characterizing the channel response via exact numerical time evolution at βJ=2βJ = 2βJ=2. Re-optimizing under the drive isolates genuine physical effects from calibration mismatch, yielding four main results: (i) distinct perturbative and non-perturbative amplitude regimes separated near ε∼J\varepsilon \sim Jε∼J; (ii) a natural low-pass filter response, with maximum fidelity suppression at ω≲β−1ω\lesssim β^{-1}ω≲β−1 and monotonic recovery above the thermal scale; (iii) a scrambling delay, evidenced by a delayed fidelity peak under an inspiral chirp (Δtscr(fid)=+0.11 J−1Δt_{\mathrm{scr}}^{(\mathrm{fid})} = +0.11\, J^{-1}Δtscr(fid)​=+0.11J−1) and independently confirmed by OTOC measurements to grow monotonically with drive amplitude; and (iv) robust, non-zero fidelity suppression across N∈{10,12,14,16}N \in \{10, 12, 14, 16\}N∈{10,12,14,16} Majorana modes. These findings establish that holographic wormholes degrade gracefully under metric-like boundary deformations, providing direct diagnostic signatures for near-term quantum hardware.
A bstract In this work, we study a type of commuting SYK model in which all terms in the Hamiltonian are commutative to each other. Because of the commutativity, this model has a large number of conserved charges and is integrable. After the ensemble average of random couplings, we can solve this model exactly in any N . Though this integral model is not holographic, we do find that it has some holography-like features, especially the near-perfect size winding in high temperatures. Therefore, we would like to call it pseudo-holographic. We also find that the size winding of this model has a narrowly peaked size distribution, which is different from the ordinary SYK model. We apply the traversable wormhole teleportation protocol in the commuting SYK model and find that the teleportation has a few features similar to the semiclassical traversable wormhole but in different parameter regimes. We show that the underlying physics is not entirely determined by the size-winding mechanism but involves the peaked-size mechanism and thermalization. Lastly, we comment on the recent simulation of the dynamics of traversable wormholes on Google’s quantum processor.
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.
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.