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

We introduce and experimentally probe a continuous interpolation parameter λ ∈ [0,1] that operationally connects integrable dynamics—characteristic of Loop Quantum Gravity (LQG)-like regimes—with maximally scrambling dynamics associated with holographic theories. The relation α(λ) = -1/2 - λ emerges independently from tensor network coarse-graining and holographic quantum error correction arguments, where α characterizes the logarithmic correction to black hole entropy. Rather than claiming an experimental realization of quantum gravity, we demonstrate that λ can be extracted from out-of-time-ordered correlator (OTOC) measurements on noisy intermediate-scale quantum (NISQ) hardware. Experiments on IBM Quantum processors across multiple circuit models—including kicked Ising, Sachdev-Ye-Kitaev (SYK), and Floquet dynamics—yield λ = 1.000 ± 0.000 for chaotic systems and λ = 0.000 ± 0.000 for integrable ones, with the formula α = -0.5 - λ exactly satisfied in all cases. Notably, Floquet circuits remain in a prethermal non-scrambling regime (λ ≈ 0), demonstrating that λ classifies the degree of scrambling, not mere non-integrability. These results establish an experimental bridge between quantum information scrambling and theoretical structures traditionally associated with quantum gravity.