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Laboratory Realization of an Analogue AdS - CFT Duality in a Cold-Atom Hyperbolic Lattice

Parker Emmerson

Published Jun 26, 2026• 0 citations
Publisher

Abstract

We present a comprehensive experimental proposal to realize a toy model ofthe AdS/CFT correspondence in a cold‑atom quantum simulator. Atwo‑dimensional hyperbolic optical lattice, generated by a combination ofstructured laser beams, hosts ultracold bosonic atoms whose hoppingamplitudes are engineered to reproduce the metric of anti‑de Sitter space(AdS$_{2+1}$). The boundary of the lattice is a one‑dimensional ring ofatoms that plays the role of the conformal field theory (CFT). Byexploiting synthetic gauge fields and Raman‑assisted tunneling, theeffective speed of light in the bulk becomes locally tunable, enablingthe simulation of the Malament–Hogarth effect---an infinite proper timewithin a finite boundary time. We detail the construction of thehyperbolic lattice, the mapping of bulk fields to boundary operators, theencoding of a universal Turing machine as a bulk defect, and the readoutof the computational halt state via boundary correlation measurementswith exponential suppression of errors. Our blueprint provides themissing laboratory platform for the PV‑crystallographic hypercomputerand opens a new paradigm for table‑top holographic quantum computation.

DOI
10.5281/zenodo.20937409

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The unification of quantum mechanics and general relativity remains one of the major open problems of theoretical physics. The Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence provides a valuable theoretical framework for this effort via a holographic duality between a theory of quantum gravity in asymptotically AdS spacetime and a conformal quantum field theory on the lower-dimensional boundary. Here, we implement a toy model of this duality called the HaPPY code, a quantum error-correcting code in the form of a tensor network with hyperbolic entanglement patterns, on a trapped-ion quantum computer. We present the first experimental confirmation of the Faulkner-Lewkowycz-Maldacena formula in this model - a key test of the holographic correspondence. We then enrich it with non-stabilizerness, or magic, and observe entropic precursors expected of emergent gravity. Finally, we present and measure a code construction whose entropic behavior is reminiscent of a highly quantum wormhole. Our experiments illustrate how quantum computers can serve as testbeds for modeling the emergence of spacetime.
We study tight-binding models in the crossover from hyperbolic to Euclidean lattices, realized through the successive insertion of Euclidean defects into hyperbolic lattices. We analyze how the holographic two-point boundary correlation function and bulk density of states evolve as defects are gradually introduced. We find that bulk properties are strongly affected by the presence of Euclidean defects, whereas boundary observables remain remarkably robust even at high defect fractions. This robustness indicates that essential features of boundary physics on hyperbolic lattices, which capture aspects of anti de-Sitter/conformal field theory (AdS/CFT)-like dualities in discrete systems, can be reproduced both experimentally and numerically without requiring perfectly hyperbolic lattices, thereby reducing the system size needed for implementation.
We propose a low energy model for simulating an analog black hole on an optical lattice using ultracold atoms. Assuming the validity of the holographic principle, we employ the Sachdev-Ye-Kitaev (SYK) model, which describes a system of randomly infinite range interacting fermions, also conjectured to be an exactly solvable UV-complete model for an extremal black hole in a higher dimensional Anti-de Sitter (AdS) dilaton gravity. At low energies, the SYK model exhibits an emergent conformal symmetry and is dual to the extremal black hole solution in near AdS2 spacetime. Furthermore, we show how the SYK maximally chaotic behaviour at large N limit, found to be dual to a gauge theory in higher dimensions, can also be employed as a non-trivial investigation tool for the holographic principle. The proposed setup is a theoretical platform to realize the SYK model with relevant exotic effects and behaviour at low energies as a highly non-trivial example of the AdS/CFT duality and a framework for studying black holes.
The PV‑crystallographic hypercomputer architecture of Emmerson~\cite{EmmersonPVHPC}requires two capabilities that were left as open assumptions: (i) embedding auniversal Turing machine (UTM) into a bulk probe inside an AdS (oreffective‑cone) temporal‑compression chamber, and (ii) reading out the haltstate on the boundary with fidelity arbitrarily close to unity at the finiteexternal deadline. This paper supplies a complete, rigorous mathematicalsolution to both. We work within the holographic quantum error‑correcting code formalism,exemplified by the HaPPY perfect‑tensor network. The bulk is a negativelycurved tensor network whose boundary is a one‑dimensional spin chain. A\emph{bulk Turing probe} is defined as a designated set of bulk logicalindices that realize a universal Turing machine, with an infinite tapeextending along the radial direction and a finite‑state head. Theholographic map encodes the entire tape and head state into the boundarywith built‑in quantum error correction. A special \emph{halt tensor}inside the network encodes the answer: if the simulated program halts, alocal operation toggles the halt tensor from ∣0⟩|0\rangle∣0⟩ to ∣1⟩|1\rangle∣1⟩;otherwise it stays at ∣0⟩|0\rangle∣0⟩. On the boundary, the halt state becomes a logical qubit protected by aholographic code of distance DDD. We define the \emph{crystallizationlatch} as a boundary operator \(\LL\) that measures this logical qubit. Bychoosing the network size appropriately, the effective error per measurementis exponentially small in DDD. Consequently, for any desired targetfidelity 1−ε1-\varepsilon1−ε, there exists a finite tensor network and afinite readout region such that the boundary latch yields the correct haltpredicate with probability at least 1−ε1-\varepsilon1−ε. The proper time ofthe probe diverges as its location approaches the conformal boundary,implementing the infinite proper‑time condition exactly. The construction isfully explicit and does not rely on any new physics beyond the standardholographic duality. Thus we complete the missing link in the PV‑crystallographic hypercomputer,establishing that a bulk universal Turing machine with high‑fidelityboundary readout is mathematically consistent and can be engineered withinthe known framework of AdS/CFT.
The PV‑crystallographic hypercomputer architecture of Emmerson~\cite{EmmersonPVHPC}requires two capabilities that were left as open assumptions: (i) embedding auniversal Turing machine (UTM) into a bulk probe inside an AdS (oreffective‑cone) temporal‑compression chamber, and (ii) reading out the haltstate on the boundary with fidelity arbitrarily close to unity at the finiteexternal deadline. This paper supplies a complete, rigorous mathematicalsolution to both. We work within the holographic quantum error‑correcting code formalism,exemplified by the HaPPY perfect‑tensor network. The bulk is a negativelycurved tensor network whose boundary is a one‑dimensional spin chain. A\emph{bulk Turing probe} is defined as a designated set of bulk logicalindices that realize a universal Turing machine, with an infinite tapeextending along the radial direction and a finite‑state head. Theholographic map encodes the entire tape and head state into the boundarywith built‑in quantum error correction. A special \emph{halt tensor}inside the network encodes the answer: if the simulated program halts, alocal operation toggles the halt tensor from ∣0⟩|0\rangle∣0⟩ to ∣1⟩|1\rangle∣1⟩;otherwise it stays at ∣0⟩|0\rangle∣0⟩. On the boundary, the halt state becomes a logical qubit protected by aholographic code of distance DDD. We define the \emph{crystallizationlatch} as a boundary operator \(\LL\) that measures this logical qubit. Bychoosing the network size appropriately, the effective error per measurementis exponentially small in DDD. Consequently, for any desired targetfidelity 1−ε1-\varepsilon1−ε, there exists a finite tensor network and afinite readout region such that the boundary latch yields the correct haltpredicate with probability at least 1−ε1-\varepsilon1−ε. The proper time ofthe probe diverges as its location approaches the conformal boundary,implementing the infinite proper‑time condition exactly. The construction isfully explicit and does not rely on any new physics beyond the standardholographic duality. Thus we complete the missing link in the PV‑crystallographic hypercomputer,establishing that a bulk universal Turing machine with high‑fidelityboundary readout is mathematically consistent and can be engineered withinthe known framework of AdS/CFT.