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

ERICK FRANCISCO PEREZ EUGENIO

Published Jan 1, 2026• 0 citations
Publisher

Abstract

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.
DOI
10.17605/osf.io/fhxnt

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The relation between loop quantum gravity (LQG) and tensor networks is explored from the perspectives of the bulk-boundary duality and holographic entanglement entropy. We find that the LQG spin-network states in a space $\mathrm{\ensuremath{\Sigma}}$ with boundary $\ensuremath{\partial}\mathrm{\ensuremath{\Sigma}}$ is an exact holographic mapping similar to the proposal in [X.-L. Qi, Exact holographic mapping and emergent space-time geometry, arXiv:1309.6282]. The tensor network, understood as the boundary quantum state, is the output of the exact holographic mapping emerging from a coarse-graining procedure of spin networks. Furthermore, when a region AAA and its complement A‾\overline{A}A are specified on the boundary $\ensuremath{\partial}\mathrm{\ensuremath{\Sigma}}$, we show that the boundary entanglement entropy S(A)S(A)S(A) of the emergent tensor network satisfies the Ryu-Takayanagi formula in the semiclassical regime, i.e., S(A)S(A)S(A) is proportional to the minimal area of the bulk surface attached to the boundary of AAA in $\ensuremath{\partial}\mathrm{\ensuremath{\Sigma}}$.
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.
Abstract We present a purely theoretical proposal, independent of any industrial collaboration, to probe out-of-time-ordered correlators OTOC (2) via information-gauge Wilson loops . Within the renormalizable unified entanglement–entropy quantum field theory (IG–RUEQFT), we treat the information current J μ info as a dynamical variable minimally coupled to an information–gauge field A μ . Our loop-based interpretation yields falsifiable predictions for holonomy responses (perimeter/area mixtures and harmonic content) near the edge of ergodicity , and specifies measurement protocols that can be instantiated on diverse quantum platforms. Building on recent OTOC(2) interferometry on superconducting processors, we design hardware-ready protocols for Google’s platform that (i) map holonomies via phase-programmable insertions, (ii) isolate large-loop (off-diagonal) interference through diagonal/off-diagonal separation, and (iii) quantify information-current fronts and flux from spatiotemporal OTOC(2) gradients. The framework yields falsifiable predictions, including loop-size scaling laws near the edge of ergodicity, phase (holonomy) response maps with harmonic structure from path ordering, and crossed-loop commutator signals diagnosing non-commutative curvature. We specify an analysis pipeline with SNR targets, bootstrap uncertainty estimates, and model selection against classical nulls (Clifford surrogates, cached Monte Carlo, tensor-network contraction), together with robustness checks to disentangle noise from genuine loop phases. The resulting experiments target a practically accessible regime in which echo-enhanced OTOC(2) retains gauge phases long enough to differentiate IG–RUEQFT loop physics from alternative explanations, enabling a concrete, platform-level test of information-gauge curvature and its role in late-time quantum interference.