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 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.
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.
Random circuit sampling (RCS) on noisy quantum hardware is widely modeled as exhibiting exponential decay of fidelity metrics (e.g., XEB, HOG) with circuit depth, converging toward Haar-random statistics beyond a characteristic noise-limited scale. This work introduces a minimal phenomenological recurrence for a coarse-grained local coherence observable defined on the qubit connectivity graph. The recurrence reproduces standard exponential decay in unstructured (fully scrambled) circuits but predicts delayed thermalization and a nonzero plateau when repeated local motifs are engineered into circuit compilation. The model introduces a single topology-dependent memory parameter α(µ), where µ denotes motif density. A transcritical bifurcation occurs when α(µ) exceeds the effective per-layer decoherence rate γ, producing a calculable plateau height and build-up depth scale. A matched-pair experimental protocol—holding qubit count, two-qubit gate count per layer, and reported hardware error rates fixed while varying only motif density—provides a direct falsification criterion. Absence of statistically significant topology dependence would rule out the model in its minimal form. The recurrence is an effective coarse-grained description at the metric level and does not modify underlying quantum channel structure or violate complete positivity.
This note presents a concrete, falsifiable prediction of Relational Field Theory (RFT) in a regime where standard open-system quantum treatments provide well-defined expectations. Consider a strongly driven open quantum system (e.g., superconducting qubit arrays or cavity-QED platforms) subject to dissipation. Under standard Lindblad or Floquet descriptions, such systems are typically expected to exhibit monotonic coherence decay or steady-state saturation without a revival mechanism of this form. RFT predicts a different outcome. Due to the adaptive domain closure T[R_c], the system’s effective response time increases in the low-coherence regime. This allows accumulated relational structure to persist long enough for the system to spontaneously re-enter a high-coherence state. The result is a non-monotonic coherence revival that arises without fine-tuning or additional parameters. Observable signatures include: Non-monotonic coherence lifetime (decay → plateau → revival) Hysteresis under drive-amplitude cycling Divergence of recovery time near a critical drive strength (critical slowing) A sharp increase in the time-quality factor Q_t=1/D_\theta The key discriminating feature is the combined appearance of these signatures. While individual behaviors may appear in nonlinear or driven systems, their joint occurrence under these conditions is not naturally predicted by standard open-system models. This prediction provides a direct experimental test of RFT. If high-precision measurements in the specified regime show only monotonic decay with no revival or hysteresis, the adaptive-closure mechanism of RFT would be ruled out. This work does not modify quantum mechanics. Instead, it proposes that coherence-constrained dynamics arising from relational persistence may constitute a cross-domain organizing structure that can be tested within existing experimental platforms.
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 project presents a clarification of earlier Relational Field Theory (RFT) work on quantum tunneling, measurement, and relational quantum gravity through the lens of recent regime-dependent coherence results. The paper argues that structure-sensitive coherence should not be interpreted as a globally active mechanism. Instead, it becomes dynamically relevant only under conditions of strong local closure, recoverability, and persistent boundary-constrained organization. The note introduces: • regime-dependent activation of structural coherence, • a closure functional for relational domains, • recoverability as a condition for persistent organization, • linearized perturbation decay inside deep-well regimes, • and stable macroscopic records as outcome-defining degrees of freedom. This framing connects recent turbulence-based computational evidence to quantum-foundations questions without claiming a universal solution to the measurement problem. It positions earlier RFT quantum papers as architectural sketches now constrained by local validity, regime dependence, and computational results.