Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Logarithmic Dependence of the OTOC Scaling Exponent on Surface Gravity: Empirical Evidence, Jones Index Structure, and AdS2 Emergence

E. F. Perez-Eugenio

Published May 3, 2026• 0 citations
Publisher

Abstract

Data, simulation scripts, and manuscript for Paper V of the Kaelion OTOC KB series. We report a logarithmic dependence of the OTOC late-time scaling exponent c on effective surface gravity κ across two independent quantum many-body models: a static SYK model at finite temperature (κ = 2πT) and a Bose-Hubbard chain with a sonic horizon (κ_sonic). The central empirical result is c = a·ln(κ) + b with R² = 0.997 (SYK) and R² = 0.988 (BH sonic), favored over c ∝ 1/κ with ΔAIC = +15.6 (OLS). The logistic β-function β(Ω) = −cΩ(1−Ω) uniquely produces AdS₂ geometry in the IR, with closed-form scalar curvature R(Ω) = −2 + 12Ω(1−Ω). Run scripts/verify_reproduction.py to confirm all key results from the authoritative JSON data files.

DOI
10.5281/zenodo.20015263

Related papers

Kaelion: Probing the LQG-Holography Transition via OTOC Measurements on Quantum Hardware

ERICK FRANCISCO PEREZ EUGENIO

Experimental verification of the Kaelion correspondence α(λ) = -1/2 - λ connecting Loop Quantum Gravity and holographic entropy corrections via OTOC measurements on IBM Quantum hardware. Includes emergent AdS₂ geometry from RG flow.

•Jan 1, 2026•0 citations

Sparsity-Independent Lyapunov Exponent in the Sachdev-Ye-Kitaev Model

Antonio M. Garcı́a-Garcı́a, Chang Liu, J. J. M. Verbaarschot

The saturation of a recently proposed universal bound on the Lyapunov exponent has been conjectured to signal the existence of a gravity dual. This saturation occurs in the low-temperature limit of the dense Sachdev-Ye-Kitaev (SYK) model, N Majorana fermions with q body (q>2) infinite-range interactions. We calculate certain out-of-time-order correlators (OTOCs) for N≤64 fermions for a highly sparse SYK model and find no significant dependence of the Lyapunov exponent on sparsity up to near the percolation limit where the Hamiltonian breaks up into blocks. This provides strong support to the saturation of the Lyapunov exponent in the low-temperature limit of the sparse SYK. A key ingredient to reaching N=64 is the development of a novel quantum spin model simulation library that implements highly optimized matrix-free Krylov subspace methods on graphical processing units. This leads to a significantly lower simulation time as well as vastly reduced memory usage over previous approaches, while using modest computational resources. Strong sparsity-driven statistical fluctuations require both the use of a much larger number of disorder realizations with respect to the dense limit and a careful finite size scaling analysis. The saturation of the bound in the sparse SYK points to the existence of a gravity analog that would enlarge substantially the number of field theories with this feature.

arXiv:2311.00639•Physical Review Letters•Aug 26, 2024•11 citations

Empirical Characterization of an Autonomous Accessibility Flow: A Universal β-Function and Continuous IR Fixed-Point Spectrum from Out-of-Time-Order Correlators

E. F. Perez-Eugenio

First release of Paper III, Kaelion OTOC KB series. Universal β-function β = −c Ω(1−Ω) confirmed across 11 quantum many-body models (slope=1.003, χ²/dof=1.11, p=0.31). Continuous IR fixed-point spectrum c ∈ [0.17, 4.30]. Pre-registered prediction c ∈ [1,4] confirmed with c = 3.41 ± 0.48 for power-law coupling J(r)=1/r. Companion papers: Paper I: https://zenodo.org/records/18752608 Paper II: https://zenodo.org/records/19105623

•Mar 22, 2026•0 citations

Correlation functions in Schwarzian liquid

Yong-Hui Qi, Yunseok Seo, Sang-jin Sin A +1 more

We analytically study low-temperature universal properties of a class of SYK-type models in the large N limit from the ${\mathrm{AdS}}_{2}$ gravity dual side in terms of $\mathrm{SL}(2,R)$-invariant Schwarzian action. The quantum correction to the conformal field theory ${\mathrm{CFT}}_{1}$ two-point correlation function due to the Schwarzian action produces a transfer of degree of freedom from the quasiparticle peak to the Hubbard band in density of states (DOS), a signature strong correlation. In Schwinger-Keldysh (SK) formalism, we calculate higher-point thermal out-of-time order correlation (OTOC) functions, which indicate quantum chaos by having a Lyapunov exponent. Higher-order local spin-spin correlations are also calculated, which can be related to the dynamical local susceptibility of quantum liquids such as the spin liquid in disordered metals, marginal Fermi liquid, non-Fermi liquid, etc.

arXiv:1804.06164•Physical review. D/Physical review. D.•Mar 5, 2019•11 citations

Emergent AdS2 Geometry from Quantum Codes

Chomiuk, Paweł

This repository contains the full dataset and analysis code accompanying the manuscript“Emergent AdS₂ Geometry from Quantum Codes: Experimental Evidence for the Fion Substrate Framework.” Using a 5-qubit ] stabilizer code implemented on IBM Quantum hardware, we reconstruct an effective information-geometric metric from 12,000 measurement shots. Bias-corrected mutual information, hyperbolic and Euclidean embeddings, stress minimization and Akaike Information Criterion (AIC) model comparison all point to a hyperbolic AdS₂ geometry with curvatureκ = −1.0012 ± 0.0039 (90% BCa CI), statistically equivalent to the theoretical value κ = −1 (TOST equivalence test, ΔAIC = 30.32 in favour of the AdS₂ model). In the associated manuscript we interpret these results within the “fion substrate framework”, a unified informational model in which elementary quantum codes generate spacetime, matter and (at high coherence) mind-like dynamics. The Figshare materials, however, focus on the quantum-information and geometric side of the work. Contents of the repository raw IBM Quantum measurement data (counts) for the 5-qubit code (12,000 shots); processed mutual-information matrices and distance matrices; Python scripts for metric embedding, bootstrap uncertainty estimation and equivalence testing (BCa + TOST); bootstrap distributions of the curvature κ and model-comparison summaries (AIC, stress); documentation on how to reproduce all numerical results and figures reported in the paper. The dataset is intended to allow full reproduction and independent re-analysis of the emergent-geometry reconstruction, and to provide a starting point for extending the protocol to larger quantum codes and higher-dimensional AdS geometries

•Jan 1, 2025•0 citations

Spacetime and Gravity as Emergent Quantum Entanglement - A Proof of Concept: Paper I — The Binary Tree Network, Exact Entropy Formula and AdS₂ Metric Convergence

Alvaro Lozano Rodriguez

This paper establishes the geometric and entropic foundations of an exactly solvable holographic model for two-dimensional quantum gravity. Taking the binary tree perfect tensor network — a hierarchical quantum system with N=2LN = 2^L N=2L boundary sites and bond dimension χ\chi χ — as its setting, it proves three main results: First, an exact closed-form formula S(Am)=f∗(m)log⁡χS(A_m) = f^*(m)\log\chi S(Am)=f∗(m)logχ is derived for the entanglement entropy of any boundary interval, where f∗(m)=min⁡(popcount2(m), 1+popcount2(Nmin⁡(m)−m))f^*(m) = \min(\mathrm{popcount}_2(m),\ 1 + \mathrm{popcount}_2(N_{\min}(m)-m)) f∗(m)=min(popcount2(m), 1+popcount2(Nmin(m)−m)) is a combinatorial function of the interval size, establishing the Ryu–Takayanagi formula as a theorem of the network rather than a conjecture. Second, the tree is shown to embed isometrically into the hyperbolic plane H2\mathbb{H}^2 H2 with every edge of equal hyperbolic length η=arccosh(21/16)\eta = \mathrm{arccosh}(21/16) η=arccosh(21/16), and the rescaled boundary metric is proved quasi-isometric to AdS2\mathrm{AdS}_2 AdS2 geodesics with explicit tight constants. Third, Newton's constant G=1/(4log⁡χ)G = 1/(4\log\chi) G=1/(4logχ) and the AdS2\mathrm{AdS}_2 AdS2 radius R=δ/ln⁡2R = \delta/\ln 2 R=δ/ln2 are derived independently from two routes — the RT formula and the embedding geometry respectively — yielding R/G=4log⁡2χR/G = 4\log_2\chi R/G=4log2χ as a proved theorem, with no free parameters once χ\chi χ is specified. The paper additionally derives the exact modular Hamiltonian of the vacuum state from the perfect tensor isometry, and recovers the bulk stress-energy tensor from boundary entropy perturbations via an explicit inversion formula, completing the chain from a discrete quantum network to a bulk metric with gravitational coupling and matter content.

•Apr 8, 2026•0 citations
Data, simulation scripts, and manuscript for Paper V of the Kaelion OTOC KB series. We report a logarithmic dependence of the OTOC late-time scaling exponent c on effective surface gravity κ across two independent quantum many-body models: a static SYK model at finite temperature (κ = 2πT) and a Bose-Hubbard chain with a sonic horizon (κ_sonic). The central empirical result is c = a·ln(κ) + b with R² = 0.997 (SYK) and R² = 0.988 (BH sonic), favored over c ∝ 1/κ with ΔAIC = +15.6 (OLS). The logistic β-function β(Ω) = −cΩ(1−Ω) uniquely produces AdS₂ geometry in the IR, with closed-form scalar curvature R(Ω) = −2 + 12Ω(1−Ω). Run scripts/verify_reproduction.py to confirm all key results from the authoritative JSON data files.
The saturation of a recently proposed universal bound on the Lyapunov exponent has been conjectured to signal the existence of a gravity dual. This saturation occurs in the low-temperature limit of the dense Sachdev-Ye-Kitaev (SYK) model, N Majorana fermions with q body (q>2) infinite-range interactions. We calculate certain out-of-time-order correlators (OTOCs) for N≤64 fermions for a highly sparse SYK model and find no significant dependence of the Lyapunov exponent on sparsity up to near the percolation limit where the Hamiltonian breaks up into blocks. This provides strong support to the saturation of the Lyapunov exponent in the low-temperature limit of the sparse SYK. A key ingredient to reaching N=64 is the development of a novel quantum spin model simulation library that implements highly optimized matrix-free Krylov subspace methods on graphical processing units. This leads to a significantly lower simulation time as well as vastly reduced memory usage over previous approaches, while using modest computational resources. Strong sparsity-driven statistical fluctuations require both the use of a much larger number of disorder realizations with respect to the dense limit and a careful finite size scaling analysis. The saturation of the bound in the sparse SYK points to the existence of a gravity analog that would enlarge substantially the number of field theories with this feature.
We analytically study low-temperature universal properties of a class of SYK-type models in the large N limit from the AdS2{\mathrm{AdS}}_{2}AdS2​ gravity dual side in terms of SL(2,R)\mathrm{SL}(2,R)SL(2,R)-invariant Schwarzian action. The quantum correction to the conformal field theory CFT1{\mathrm{CFT}}_{1}CFT1​ two-point correlation function due to the Schwarzian action produces a transfer of degree of freedom from the quasiparticle peak to the Hubbard band in density of states (DOS), a signature strong correlation. In Schwinger-Keldysh (SK) formalism, we calculate higher-point thermal out-of-time order correlation (OTOC) functions, which indicate quantum chaos by having a Lyapunov exponent. Higher-order local spin-spin correlations are also calculated, which can be related to the dynamical local susceptibility of quantum liquids such as the spin liquid in disordered metals, marginal Fermi liquid, non-Fermi liquid, etc.
This repository contains the full dataset and analysis code accompanying the manuscript“Emergent AdS₂ Geometry from Quantum Codes: Experimental Evidence for the Fion Substrate Framework.” Using a 5-qubit ] stabilizer code implemented on IBM Quantum hardware, we reconstruct an effective information-geometric metric from 12,000 measurement shots. Bias-corrected mutual information, hyperbolic and Euclidean embeddings, stress minimization and Akaike Information Criterion (AIC) model comparison all point to a hyperbolic AdS₂ geometry with curvatureκ = −1.0012 ± 0.0039 (90% BCa CI), statistically equivalent to the theoretical value κ = −1 (TOST equivalence test, ΔAIC = 30.32 in favour of the AdS₂ model). In the associated manuscript we interpret these results within the “fion substrate framework”, a unified informational model in which elementary quantum codes generate spacetime, matter and (at high coherence) mind-like dynamics. The Figshare materials, however, focus on the quantum-information and geometric side of the work. Contents of the repository raw IBM Quantum measurement data (counts) for the 5-qubit code (12,000 shots); processed mutual-information matrices and distance matrices; Python scripts for metric embedding, bootstrap uncertainty estimation and equivalence testing (BCa + TOST); bootstrap distributions of the curvature κ and model-comparison summaries (AIC, stress); documentation on how to reproduce all numerical results and figures reported in the paper. The dataset is intended to allow full reproduction and independent re-analysis of the emergent-geometry reconstruction, and to provide a starting point for extending the protocol to larger quantum codes and higher-dimensional AdS geometries
This paper establishes the geometric and entropic foundations of an exactly solvable holographic model for two-dimensional quantum gravity. Taking the binary tree perfect tensor network — a hierarchical quantum system with N=2LN = 2^L N=2L boundary sites and bond dimension χ\chi χ — as its setting, it proves three main results: First, an exact closed-form formula S(Am)=f∗(m)log⁡χS(A_m) = f^*(m)\log\chi S(Am)=f∗(m)logχ is derived for the entanglement entropy of any boundary interval, where f∗(m)=min⁡(popcount2(m), 1+popcount2(Nmin⁡(m)−m))f^*(m) = \min(\mathrm{popcount}_2(m),\ 1 + \mathrm{popcount}_2(N_{\min}(m)-m)) f∗(m)=min(popcount2(m), 1+popcount2(Nmin(m)−m)) is a combinatorial function of the interval size, establishing the Ryu–Takayanagi formula as a theorem of the network rather than a conjecture. Second, the tree is shown to embed isometrically into the hyperbolic plane H2\mathbb{H}^2 H2 with every edge of equal hyperbolic length η=arccosh(21/16)\eta = \mathrm{arccosh}(21/16) η=arccosh(21/16), and the rescaled boundary metric is proved quasi-isometric to AdS2\mathrm{AdS}_2 AdS2 geodesics with explicit tight constants. Third, Newton's constant G=1/(4log⁡χ)G = 1/(4\log\chi) G=1/(4logχ) and the AdS2\mathrm{AdS}_2 AdS2 radius R=δ/ln⁡2R = \delta/\ln 2 R=δ/ln2 are derived independently from two routes — the RT formula and the embedding geometry respectively — yielding R/G=4log⁡2χR/G = 4\log_2\chi R/G=4log2χ as a proved theorem, with no free parameters once χ\chi χ is specified. The paper additionally derives the exact modular Hamiltonian of the vacuum state from the perfect tensor isometry, and recovers the bulk stress-energy tensor from boundary entropy perturbations via an explicit inversion formula, completing the chain from a discrete quantum network to a bulk metric with gravitational coupling and matter content.