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Spatial Scrambling Profiles and System-Size Scaling of the Scrambling Residual Omega

E. F. Perez-Eugenio

Published Mar 19, 2026• 0 citations
Publisher

Abstract

Data, simulation code, and figures for: "Spatial Scrambling Profiles and System-Size Scaling of the Scrambling Residual Ω across Dynamical Regimes: Exact Simulation and Cross-Platform Quantum Hardware Validation" E. F. Perez-Eugenio (2026) This repository contains exact statevector simulations (N=4-18) of five dynamical models (KI chaotic, KI mixing, KI integrable, KI dual-unitary, SYK-inspired), cross-platform quantum hardware measurements (IBM Heron, Rigetti Ankaa-3, AQT IBEX Q1), and analysis scripts for the Ω scrambling diagnostic. Key results: spatial scrambling profiles Ω(r), 15× ion trap fidelity advantage over superconducting hardware, and first empirical characterization of an autonomous accessibility flow from quantum hardware. Companion to Paper I: https://doi.org/10.5281/zenodo.18752608

DOI
10.5281/zenodo.19105622

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Data, simulation code, and figures for: "Spatial Scrambling Profiles and System-Size Scaling of the Scrambling Residual Ω across Dynamical Regimes: Exact Simulation and Cross-Platform Quantum Hardware Validation" E. F. Perez-Eugenio (2026) This repository contains exact statevector simulations (N=4-18) of five dynamical models (KI chaotic, KI mixing, KI integrable, KI dual-unitary, SYK-inspired), cross-platform quantum hardware measurements (IBM Heron, Rigetti Ankaa-3, AQT IBEX Q1), and analysis scripts for the Ω scrambling diagnostic. Key results: spatial scrambling profiles Ω(r), 15× ion trap fidelity advantage over superconducting hardware, and first empirical characterization of an autonomous accessibility flow from quantum hardware. Companion to Paper I: https://doi.org/10.5281/zenodo.18752608
Preprint: This work is a preprint, has not undergone peer review, and is made publicly available to establish a public scientific record. This publication presents a hardware validation of a minimal, sign-based operational consequence of the Dynamical Information Geometry (DIG) framework on real quantum devices. The work introduces no new theory and no numerical modeling. Instead, it tests a single operational hypothesis (OD-DIG-H1) on heterogeneous quantum hardware platforms, including IBM Quantum and AWS Braket (IonQ). The operational quantity tested is the sign of the leakage differenceΔLeak = Leak_LENS − Leak_CTRL,with leakage defined as Leak = 1 − P(b_ref). The reference bitstring is defined per run as b_ref = mode(CTRL), ensuring a hardware-agnostic reference choice. For all included hardware runs, the observed sign of ΔLeak is positive under the stated operational definition. The analysis is deliberately restricted to sign-only reporting and excludes fitting procedures, noise mitigation, or quantitative cross-platform comparisons. The results are supported by a publicly available, immutable hardware dataset archived on Zenodo. Related works (for reference and context): DIG Part I (theoretical framework):https://doi.org/10.5281/zenodo.17983399 DIG Part II (numerical validation):https://doi.org/10.5281/zenodo.17982058 DIG — N1 (definitions and scope):https://doi.org/10.5281/zenodo.18001179 Dynamical Information Geometry (DIG) – Hardware Validation Dataset:https://doi.org/10.5281/zenodo.18099420 DIG Part IV (regime structure and operational context):https://doi.org/10.5281/zenodo.18202656 DIG Part V (multidimensional formulation):https://doi.org/10.5281/zenodo.18210315 DIG Part VI (scaling 1D hardware validation): https://doi.org/10.5281/zenodo.18226369 DIG Part VII Dynamical Information Geometry:Two-Dimensional Twin-Sign Validation under Fixed Audit and Regime Constraintshttps://doi.org/10.5281/zenodo.18313460 DIG — N2 (definitions/interpretation/non-equivalences) https://doi.org/10.5281/zenodo.18380514 Correspondence regarding this work may be directed to:kaya@cab-film.com
Preprint: This work is a preprint, has not undergone peer review, and is made publicly available to establish a public scientific record. This publication presents operational one-dimensional scaling tests of the Dynamical Information Geometry (DIG) framework using the Twin-Test protocol. Dynamical Information Geometry assigns an effective, state-dependent geometry to quantum many-body dynamics based on the spatial organization of mutual information. Earlier parts of the DIG series established the theoretical framework, provided numerical validation, introduced hardened operational definitions, and clarified regime structure and necessity. The present work, DIG Part VI, does not introduce new theory, new observables, or new numerical modeling. Its role is strictly operational. It documents how the Twin-Test protocol behaves under controlled one-dimensional scaling variations along two independent axes: system-size increase in a simulator implementation and circuit-depth increase in a quantum hardware implementation. Both scaling axes are evaluated within the same operational framework, using the mandatory audit logic defined in DIG Part IV. No attempt is made to relate or map these axes onto one another. The analysis is restricted to structural sign behavior, audit classification (marker-stable versus marker-transfer), and the identification of an operational robustness limit (defect) at increased depth. No universal scaling laws are proposed. No fitting, extrapolation, or cross-platform amplitude matching is performed. All operational definitions and decision rules are stated explicitly in the manuscript. The accompanying dataset implements these rules verbatim and enables deterministic third-party reproduction without interpretation. Related works (for reference and context): DIG Part I (theoretical framework):https://doi.org/10.5281/zenodo.17983399 DIG Part II (numerical validation):https://doi.org/10.5281/zenodo.17982058 DIG Part III (hardware validation):https://doi.org/10.5281/zenodo.18100057 DIG Part IV (regime structure and operational necessity):https://doi.org/10.5281/zenodo.18202656 DIG Part V (multidimensional formulation):https://doi.org/10.5281/zenodo.18210315 DIG Part VI Data Set: https://doi.org/10.5281/zenodo.18226272 DIG Part VII Dynamical Information Geometry:Two-Dimensional Twin-Sign Validation under Fixed Audit and Regime Constraintshttps://doi.org/10.5281/zenodo.18313460 DIG — N1 (definitions, scope, and non-equivalences):https://doi.org/10.5281/zenodo.18001179 Correspondence regarding this work may be directed to:kaya@cab-film.com
PROBING THE MSS BOUND AND SCRAMBLING DYNAMICS IN A MINIMAL 3-QUBIT SYSTEM ABSTRACT:This study investigates the fundamental limits of quantum chaos—the Maldacena-Shenker-Stanford (MSS) bound—using a minimal 3-qubit non-integrable system[cite: 82, 87]. By prioritizing measurement precision (16,384 shots) over system size on the IBM Quantum Torino processor, I resolve the complete "scrambling life-cycle," including the chaotic burst and the finite-size recurrence of quantum complexity[cite: 89, 91]. The extracted intrinsic Lyapunov exponent (1.30 +/- 0.05) satisfies the MSS bound in the infinite-temperature limit[cite: 90]. These results demonstrate that minimal quantum hardware can probe deep holographic principles and provide a high-precision benchmark for quantum gravity simulations[cite: 92]. KEY SCIENTIFIC ADVANCES:- Intrinsic Lyapunov Extraction: Utilized non-linear data collapse and bootstrap analysis to isolate the scrambling rate from finite-size effects[cite: 138, 140].- Observation of Unitary Recurrence: Resolved the late-time revival of information fidelity at t=3, a hallmark of unitary dynamics in finite Hilbert spaces[cite: 131, 132].- MSS Bound Verification: Defined an effective scrambling temperature scale to confirm adherence to the universal chaos bound[cite: 147, 148]. REPOSITORY CONTENTS:1. Manuscript & SI: Complete text and detailed quantum circuit sequences.2. Raw Experimental Data: Execution counts (shots) from the IBM Quantum Torino processor[cite: 64, 118].3. Analysis Scripts: Python scripts for data collapse fitting and Lyapunov exponent extraction[cite: 64, 139]. NOTE:This work serves as the foundational technical benchmark for larger-scale holographic simulations on NISQ devices[cite: 160].
This preprint presents a Kuramoto--XY synchronisation study with heterogeneous natural frequencies, simulator baselines, and ledgered IBM Heron r2 evidence. A Rust/PyO3-assisted pipeline supports entanglement entropy, Krylov complexity, OTOC scrambling, and Floquet discrete-time-crystal diagnostics for 2--16 qubit systems. The manuscript reports finite-size diagnostics consistent with Berezinskii--Kosterlitz--Thouless scaling in the small systems studied, including a periodic-boundary central-charge estimate near c = 1 at n = 8, while explicitly noting finite-size drift at larger sizes. It also records subharmonic Floquet response, non-ergodic level-spacing behaviour for heterogeneous frequencies, and a hardware-anchored scaling analysis that bounds exact Hilbert-space simulation costs. The record archives the manuscript source and PDF. Legacy IBM artefacts are treated as committed artefact-path evidence rather than aggregate validation, and the resource-boundary discussion is not promoted as a broad quantum-advantage claim because classical Rust Kuramoto ODE baselines remain faster in the measured observable-level regime.