REGISTRATION PREPRINT NOTE This record is the formal abstract (v0.2) announcing the CoherentialHamming Law, a named operational regularity for Hamming-distancecoherence decay in multi-qubit quantum hardware under localindependent dephasing. The full paper — including per-platform experimental tables, sixfigures, methodology section, complete statistical analysis, andreferences list — is in preparation and will be submitted toQuantum (the open journal for quantum science) as primary targetand Physical Review Research as secondary target within 2026 Q2. The theoretical foundations (Hamming Decay Theorem, bridge D_K → d_H)are available in the author's prior work:— P0/GHZ-Bridge v2.0 (DOI: 10.5281/zenodo.19009933)— P1 v1.1 (DOI: 10.5281/zenodo.19020842)— P1-bis v1.0 (March 2026) Raw cross-platform experimental data supporting the validation areavailable in:— GHZ Cross-Platform v4.1 PLATINUM (DOI: 10.5281/zenodo.18307211) This abstract establishes the formal naming and operational framingof the Coherential Hamming Law. The full paper will provide thecomplete experimental and statistical expedient.
REGISTRATION PREPRINT NOTE This record is the formal abstract (v0.2) announcing the CoherentialHamming Law, a named operational regularity for Hamming-distancecoherence decay in multi-qubit quantum hardware under localindependent dephasing. The full paper — including per-platform experimental tables, sixfigures, methodology section, complete statistical analysis, andreferences list — is in preparation and will be submitted toQuantum (the open journal for quantum science) as primary targetand Physical Review Research as secondary target within 2026 Q2. The theoretical foundations (Hamming Decay Theorem, bridge D_K → d_H)are available in the author's prior work:— P0/GHZ-Bridge v2.0 (DOI: 10.5281/zenodo.19009933)— P1 v1.1 (DOI: 10.5281/zenodo.19020842)— P1-bis v1.0 (March 2026) Raw cross-platform experimental data supporting the validation areavailable in:— GHZ Cross-Platform v4.1 PLATINUM (DOI: 10.5281/zenodo.18307211) This abstract establishes the formal naming and operational framingof the Coherential Hamming Law. The full paper will provide thecomplete experimental and statistical expedient.
We provide a minimal analytic framework, entirely within standard open-quantum-system theory, that explains the protocol-robust GHZ advantage observed experimentally across heterogeneous quantum platforms. The framework rests on three results: (1) the Hamming Decay Theorem, showing that off-diagonal density matrix elements decay as lambda^{d_H} under any local quantum channel; (2) a binomial derivation of the product-state fidelity F_prod = [(1+exp(-gamma*t))/2]^N under the IBM protocol; and (3) a unification of the two experimental regimes (IBM dephasing-dominated and IonQ amplitude-damping-dominated) via T2-blindness of the GHZ observable. A three-parameter noise model calibrated to IonQ 5-qubit data reproduces the selectivity pattern GHZ+, W-, Cluster- with correct signs. The structural invariant S(rho) captures the channel-independent topology underlying the advantage. Includes Appendix A: Revised Empirical Basis with cross-platform convergence data, selectivity tables, hardware threshold, and kill switches.
This is the academically citable, open-access companion to the printed monograph "Enticuant: Book IX of the RCD 2.0 Program — Five Chapters on Coherence: Geometry, Thermodynamics, and Empirical Law" (Arturo Cerezo García, Quantum Benchmark Insights, May 2026, ISBN-13 979-8195474782). Book IX of the RCD 2.0 program (Radial Coherential Dynamics) introduces and consolidates a new conceptual term — the enticuant — and gathers five chapters that the program took two years to earn. Not by speculation. By measurement, by calculation, by verification across multiple independent quantum hardware platforms. The enticuant names what the coherential field C(x,t) becomes when it crosses from formal scalar to operational object: when its decoherence is organized by the Hamming distance, when its irreversibility is measured on real quantum machines, when its geometric counterpart in disformal gravity is bounded by mathematical theorem. Five chapters, five verbs: — RELOCATE: GHZ entanglement is moved from theoretical center to coherential limit (Chapter VI), based on a five-platform validation campaign on IBM Heron, IonQ Forte, Rigetti Ankaa-3, IQM Garnet, and IQM Emerald. — SITUATE: RCD is positioned with respect to the Standard Model (Chapter VII), declaring four explicit walls the program does not cross. — NAME: The Coherential Hamming Law (Chapter VIII), a transversal empirical regularity verified on five quantum architectures with statistical significance p ≈ 7×10⁻²⁷. — MEASURE: The first structured experimental measurement of the coherential component of irreversible entropy Ξ on commercial NISQ hardware (Chapter IX), with a six-point curve on IBM ibm_fez. — PROVE: A mathematical theorem of disformal subluminality with dust (Chapter X), demonstrating that the scalar sound speed in DHOST gravity is subluminal in any astrophysically relevant environment, with explicit GW170817 compatibility. Each chapter integrates a guest voice — Hamming, Heraclitus, Boltzmann, Newton, Lao Tzu, Vera Rubin, and others — acknowledging the program's debt to twenty-five centuries of rigorous thought. The complete book consists of: Threshold, Foreword, Prologue ("La Idea Antes de la Idea"), and ten integrated chapters (I — The Coherential Field; II — Coherential Perturbations; III — Gravitational Coupling; IV — The Enticuant; V — Geodesometry of Coherence; VI — GHZ as Coherential Limit; VII — Two Scalar Fields; VIII — Coherential Hamming Law; IX — Thermodynamics of Coherence; X — Geometry of Coherence). All raw experimental data referenced in the book is publicly deposited on Zenodo. The measurement remains the arbiter. Five chapters, five verbs: Relocate · Situate · Name · Measure · Prove. This Zenodo deposit makes the full text openly available under CC-BY 4.0 alongside the printed paperback edition, enabling academic citation, indexing in OpenAIRE, and integration into the broader RCD 2.0 program registry on Zenodo.
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
This work introduces the geodesometry of coherence, a minimal discrete dynamical extension of the Hamming Decay Theorem in quantum state spaces. The Hamming Decay law establishes that off-diagonal elements of a density matrix decay exponentially with Hamming distance under local noise channels. However, this metric does not account for the physical structure through which coherence is lost. In this work, the Hamming hypercube is endowed with anisotropic physical weights on its edges, representing local noise, coupling asymmetry, or entropic cost. A minimal 3-qubit model with non-uniform weights (3, 2, 1) demonstrates that pairs of states with equal Hamming distance can exhibit different accumulated transition costs, leading to a falsifiable prediction: equal Hamming distance does not necessarily imply equal decoherence rate under anisotropic conditions. Explicit GO/KILL conditions are defined, and a minimal experimental protocol is proposed. The formulation is deliberately restricted to the quantum discrete sector and does not claim extension to gravity, cosmology, or gauge theories. It is presented as a falsifiable intermediate step between: Hamming geometry (metric structure), geodesometry (discrete dynamics), and a potential continuous effective action Seff[C]S_{\mathrm{eff}}[C]Seff[C] within the Radial Coherential Dynamics (RCD) program. This work is intended as a minimal, testable framework rather than a complete theory.
Meta-Analysis — Applied Quantum Computing Track This record presents a unifying meta-analysis of applied benchmarks within the Radial Coherential Dynamics (RCD) research program, synthesizing results across multiple quantum algorithms, system dimensionalities, and problem classes under a single coherence-regulation principle. Building upon the foundational decoherence suppression model (Topological Decoherence Suppression via Coherential Geometry, Zenodo, December 2025, DOI: 10.5281/zenodo.18000641), and its applied benchmarks in variational and optimization algorithms, this work consolidates evidence that a fixed decoherence scaling law T2→T2/αT_2 \rightarrow T_2/\sqrt{\alpha}T2→T2/α (with α≈1.3×10−4\alpha \approx 1.3 \times 10^{-4}α≈1.3×10−4) produces consistent, non-ad-hoc improvements across NISQ-relevant tasks. The meta-analysis integrates four independent benchmarks: (i) VQE for molecular H₄ (0D), (ii) VQE for a graphene-inspired hexagon (2D, PBC), (iii) VQE for a 1D Hubbard chain (OBC), and (iv) QAOA for MaxCut optimization on graphs. All benchmarks employ a controlled A/B methodology in which identical circuits are executed with standard noise (control) and coherence-regulated noise (treatment), with no parameter tuning introduced at the benchmark level. Across these diverse settings, coherence regulation yields stable reductions in energy error (≈ 40–46% for VQE tasks) and optimization gap (≈ 25% for QAOA), with magnitudes consistent with the underlying decoherence scaling and robust to changes in topology, dimensionality, and algorithmic structure. This work does not introduce new physical assumptions or experimental claims. Rather, it provides a consolidated, cross-domain view intended to clarify scope, consistency, and limitations, and to facilitate independent assessment and downstream reuse by the scientific community. All figures, summary data, and benchmark references are provided for transparency and reproducibility.
Quantum Resonance Theory (QRT; Anson 2024, DOI https://doi.org/10.5281/zenodo.21263717) predicts that superconducting-qubit coherence increases by 5–10% under a periodic physical drive at ωr = 10 MHz with amplitude R0 = 10⁻³ rad. A prior execution of this design (v4, job d940k9lgc6cc73feh290, July 2026) was found post-hoc to contain two implementation flaws — condition-to-qubit position confounding from incomplete rotation, and a decay-only fit model unable to represent Ramsey fringes from residual per-qubit detuning (~50–85 kHz observed) — and its verdict was withdrawn as improperly derived rather than claimed. This registration corrects the implementation with the hypothesis, parameters, frequencies, and drive amplitude unchanged: (1) full six-fold condition-to-qubit rotation, so every condition visits every physical qubit and position effects cancel in same-qubit contrasts; (2) a model-free primary index — the coherence-envelope area, the integral of |P(0) − 0.5| over the delay grid — which is monotone in coherence time, immune to fringe phase and detuning, and requires no curve fitting; (3) a same-qubit paired difference contrast as the primary comparison, which the v4 dataset demonstrated is the only clean comparison on this hardware. The drive is delivered as native fractional RX pulses (physical microwave drive) with a preregistered physicality assertion. Six conditions (four off-resonance frequencies, the theory-designated 10 MHz, and an undriven descriptive reference) run in parallel across six qubits per circuit. The result will be published regardless of outcome.