Coherence measurements as high as 0.9995 on IBM hardware and 0.975 on Rigetti—persisting even at extreme single-qubit depths up to 2048 H–S–H blocks—define an empirical outlier far beyond anything predicted by standard decoherence models. This stability emerges precisely where contemporary theory expects rapid collapse toward mixed states, yet the circuits remain sharply ordered and depth-insensitive. This behavior is empirically and mathematically congruent with the two-parameter unified Kālīon Field, a scalar–tensor framework shown to resolve the Hubble tension, reproduce the MOND acceleration law, unify dark-sector phenomenology, reduce quantum entropy, preserve coherence under non-unital evolution, constrain vacuum curvature, and organize gravitational–informational dynamics within a single coupled structure. The paper presents the anomaly independently of interpretation: fidelities and entropies are reconstructed directly from raw IBM and Rigetti outputs; the full dataset shows no monotonic decay toward the p₀ = 0.5 baseline; and the significance relative to a mixed-state null is extreme. The alignment with the Kālīon predictions is documented but not presupposed. All raw data, circuit reconstructions, and analysis scripts accompany this Zenodo deposit for full replication and scrutiny.
Coherence measurements as high as 0.9995 on IBM hardware and 0.975 on Rigetti—persisting even at extreme single-qubit depths up to 2048 H–S–H blocks—define an empirical outlier far beyond anything predicted by standard decoherence models. This stability emerges precisely where contemporary theory expects rapid collapse toward mixed states, yet the circuits remain sharply ordered and depth-insensitive. This behavior is empirically and mathematically congruent with the two-parameter unified Kālīon Field, a scalar–tensor framework shown to resolve the Hubble tension, reproduce the MOND acceleration law, unify dark-sector phenomenology, reduce quantum entropy, preserve coherence under non-unital evolution, constrain vacuum curvature, and organize gravitational–informational dynamics within a single coupled structure. The paper presents the anomaly independently of interpretation: fidelities and entropies are reconstructed directly from raw IBM and Rigetti outputs; the full dataset shows no monotonic decay toward the p₀ = 0.5 baseline; and the significance relative to a mixed-state null is extreme. The alignment with the Kālīon predictions is documented but not presupposed. All raw data, circuit reconstructions, and analysis scripts accompany this Zenodo deposit for full replication and scrutiny.
This note presents an RFT interpretation of an anomalous coherence persistence effect reported publicly in 2025 RCS benchmark data. Standard quantum-circuit expectations predict full thermalisation on noisy 16-qubit superconducting hardware by depth ~30, driving XEB toward zero and eliminating internal structure. Instead, the publicly reported metrics indicated XEB > 4, HOG > 0.8, and a measurable entropy deficit, revealing structured attractors in a regime where standard models predict complete chaotic dispersion. Relational Field Theory (RFT) provides a natural theoretical explanation for this behavior: the reported anomaly matches the expected signatures of a system entering a deep curvature-stiffened coherence well in the universal scalar field 𝑅 𝑐 R c , allowing attractor structure and causal memory to persist far beyond the expected decoherence horizon. This analysis presents a minimal RFT interpretation based solely on publicly released benchmark metrics. Note: This analysis uses only publicly released circuit metrics. It makes no claims about proprietary architectures, internal mechanisms, trade secrets, or patented methods. No inference is made about the mechanisms or design intentions of QSCE or any other proprietary system.
This technical note documents the numerical stability of a two-peak (Z-level) interference pattern observed in a fixed 29-qubit quantum circuit. The analysis was performed using the Qiskit AerSimulator backend under controlled conditions, including variations in shot count and phase-parameter offsets. The results demonstrate that the observed interference structure is reproducible, robust against sampling fluctuations, and not dependent on fine-tuned parameter choices. This document does not present a theoretical proof or physical interpretation. Its sole purpose is to provide an empirical numerical reference for the stability and reproducibility of the observed interference pattern, serving as a supporting record for related theoretical and conceptual works by the author. In version v3, the numerical analysis is extended beyond 63 qubits up to 79 qubits by employing reduced statistical descriptors rather than full state-space representations. This extension demonstrates that the observed Z-level interference stability persists under scalable statistical evaluation, without requiring exponentially growing state-vector simulations. Additional clarification The reported “Z-level progress” refers to an internal, relative coverage metric within the author’s numerical stability framework. It is not a physical completeness measure, nor a claim of global optimality. Earlier high-percentage stability values (e.g. 95–98%) correspond to local robustness indicators such as sampling consistency, seed invariance, and phase-noise tolerance within fixed parameter windows. The lower percentage reported here reflects a stricter, global aggregation across multiple independent stability dimensions. This distinction is intentional and avoids conflating local robustness with global domain coverage. This work reports a numerical stability certificate for X–Z basis statistical divergence measures obtained in controlled simulations. A multiscale grid and zoom analysis identifies a non-trivial stable phase-offset interval (pj ∈ [0.038, 0.052]) in which total variation distance, Shannon entropy, and directed Kullback–Leibler divergences remain reproducible under changes in sampling depth, random seed, and numerical resolution. A persistent directional asymmetry between KL_XZ and KL_ZX is numerically observed across all tested scales. This document reports numerical results only and does not claim physical realization, theoretical proof, or universal validity. Interpretational note: The absence of a direct Lorentz-covariant or gauge-field embedding should not be interpreted as a deficiency of the numerical results, but as a limitation of applying classical spacetime questions to an emergent, resonance-based stability structure. The reported Z-level behavior constrains the space of viable physical interpretations rather than completing one.
This work presents a phenomenological, RFT-inspired coherence model for entanglement stability in open quantum systems. A scalar quantity R_c(t)is introduced as a coarse-grained descriptor of phase-aligned correlation structure, motivated by off-diagonal density-matrix coherence but not intended to replace standard measures such as concurrence, negativity, or entanglement entropy. The model proposes a first-order dynamical equation balancing effective decoherence against interaction-driven coherence restoration. Numerical experiments in controlled classical fields are used as structural analogues, not direct quantum simulations. These experiments show that coherence-like behavior can separate into gradient-based intensity components and structure-tensor components that respond differently to shear- and vortex-dominated geometries. The results support a multi-component view of coherence in which stability may depend not only on scalar magnitude but also on geometric organization. The framework is exploratory and phenomenological, intended to motivate future comparison with full Lindblad/open-system simulations and experimental quantum platforms.
Standard Random Circuit Sampling (RCS) predicts full thermalization at sufficient depth, with output distributions converging rapidly toward uniform noise under realistic hardware conditions. Yet several recent experimental results have displayed unexpected persistence of structured output distributions far beyond the expected decoherence horizon. This paper presents a vendor-agnostic benchmark demonstrating that such persistence is not an architectural anomaly, but a direct signature of a deep Rc coherence well as defined in Relational Field Theory (RFT). Rc wells arise when curvature-stiffened regions of the universal scalar field resist chaotic dispersion, enabling stable probability attractors even in circuits where standard quantum dynamics predict complete entropy saturation. We provide a minimal, architecture-independent circuit that any quantum hardware vendor can execute to detect Rc well behavior. The benchmark uses symmetric entanglers, global phase rotation, chaotic scrambling, and convergence layers to probe curvature-stiffened regimes. Four measurable signatures—XEB decay behavior, entropy suppression, HOG persistence, and inverse participation ratio (IPR)—constitute a clear, falsifiable Rc-well fingerprint. This work generalizes beyond any specific architecture and requires no specialized routing, collapse engineering, or deterministic control systems. It offers the first universal test for detecting Rc-governed coherence persistence and forms a reproducible foundation for cross-vendor validation of RFT predictions
This paper presents the application of Relational Field Theory (RFT) to random circuit sampling (RCS), a standard benchmark in quantum computing. Building on the reduced relational law: {\dot{R}}_c=-\lambda R_c+F_{int},\bigm and the operational coherence functional: R_c=\alpha\cdot\beta\cdot\gamma,\bigm the framework is applied to reported RCS data from superconducting qubit experiments. Within this setting: α corresponds to distribution sharpness (e.g., cross-entropy benchmark or peak statistics) β reflects circuit connectivity and gate structure γ captures persistence across circuit depth and repeated runs Using published results, the relational coherence functional is evaluated against observed behaviors in RCS systems, including: Persistence of structured output distributions beyond expected circuit depth Formation of coherence wells, where structure remains stable under noise Attractor-like clustering of high-probability output states Suppression of entropy relative to fully randomized expectations These observations are consistent with the four falsifiable predictions introduced in RFT v2.0: critical slowing near coherence thresholds hysteresis-like behavior under parameter variation persistence in coherence wells emergence of structural anchors This work does not modify quantum mechanics or attempt to reproduce standard RCS results. Instead, it provides a structural interpretation of observed behavior using a coherence-based framework applied to existing experimental data. The results extend Relational Field Theory from classical and toy-model systems into the quantum domain, supporting its potential as a cross-domain framework for understanding persistence, structure, and transition dynamics.
Relational Field Theory (RFT) models quantum computing as emergent coherence dynamics, reframing qubits, entanglement, and decoherence as phenomena of residue fields 𝑅𝑐 (𝑥, 𝑡). Unlike conventional hardware-dependent approaches, RFT offers a complementary perspective, suggesting coherence stabilization via minimal 𝜆(𝑥, 𝑡), potentially easing environmental constraints. Qubit states and entanglement arise from 𝑅𝑐 (𝑥, 𝑡) configurations, while decoherence is expressed as residue field decay via 𝜆(𝑥, 𝑡). This framework complements existing quantum architectures and proposes testable alternatives to current hardware limits. We predict measurable residue anomalies in Bose-Einstein condensates (BECs) (Δ𝑅𝑐 = (1.0 ± 0.2) × 1029 J/m3) and potential signatures in hybrid quantum-classical systems, offering a roadmap for testing RFT’s relevance to quantum information processing. We invite experimental scrutiny to explore whether coherence dynamics can unify quantum computing, thermodynamics, and cosmology under a single framework Provenance: Originally published on Zenodo (Aug 2025). 10.5281/zenodo.16790423