We derive the effective exchange coupling J₁₂ between two superconducting qubits mediated by a tunable coupler using a controlled Schrieffer-Wolff transformation in the dispersive regime. This derivation establishes the microscopic origin of the coherent gain parameter J appearing in the Radial Coherential Dynamics (RCD) master equation. We demonstrate that the universality hypothesis α ≡ Γ/J ~ 10⁻⁴ becomes consistent and experimentally falsifiable when explicitly restricted to high-coherence hardware operating with T₂_swap ≥ 200 μs and tunable exchange couplings J₁₂ ~ 10-40 MHz. Cross-platform analysis of recent experimental data (IBM Heron/Nighthawk, Google Willow, Rigetti Ankaa-3, IQM) reveals that state-of-the-art devices are entering the regime where the universality test becomes meaningful. The corrected prediction—Γ_swap ~ 1-5 kHz—is consistent with IBM Nighthawk's reported T₁ ~ 350 μs. This paper closes the logical gap between microscopic Hamiltonians and the effective coherence dynamics postulated in RCD, while establishing concrete falsification criteria. Part of the Radial Coherential Dynamics (RCD) Paper Series.
We derive the effective exchange coupling J₁₂ between two superconducting qubits mediated by a tunable coupler using a controlled Schrieffer-Wolff transformation in the dispersive regime. This derivation establishes the microscopic origin of the coherent gain parameter J appearing in the Radial Coherential Dynamics (RCD) master equation. We demonstrate that the universality hypothesis α ≡ Γ/J ~ 10⁻⁴ becomes consistent and experimentally falsifiable when explicitly restricted to high-coherence hardware operating with T₂_swap ≥ 200 μs and tunable exchange couplings J₁₂ ~ 10-40 MHz. Cross-platform analysis of recent experimental data (IBM Heron/Nighthawk, Google Willow, Rigetti Ankaa-3, IQM) reveals that state-of-the-art devices are entering the regime where the universality test becomes meaningful. The corrected prediction—Γ_swap ~ 1-5 kHz—is consistent with IBM Nighthawk's reported T₁ ~ 350 μs. This paper closes the logical gap between microscopic Hamiltonians and the effective coherence dynamics postulated in RCD, while establishing concrete falsification criteria. Part of the Radial Coherential Dynamics (RCD) Paper Series.
The quantum computing narrative has been dominated by speed. This paper argues that the fundamental quantum resource is not computational acceleration but coherence maintenance. We demonstrate that the RCD framework reveals a characteristic coherence ratio α ≡ Γ/J appearing across radically different physical domains: superconducting qubits (~10⁻⁴), cosmological dark energy (~10⁻⁴), and neural systems (~0.1, critical regime). The universality refers to the structural form α = Γ/J and the necessity of N-signatures, not to a single numerical value. Key thesis: "RCD does not exploit quantum computers to compute more, but to remain coherent longer in regimes where classical control fails." This paper closes the XIV series by unifying mathematical foundations (XIV-A), cosmological application (XIV-B), impossibility theorem (XIV-C), and first-principles derivation (XIV-D) into a cross-domain framework with unified falsifiability criteria. Part of the XIV Series:- XIV-A: Structure (DOI: 10.5281/zenodo.18207097)- XIV-B: Cosmology (DOI: 10.5281/zenodo.18207197)- XIV-C: Necessity (DOI: 10.5281/zenodo.18207252)- XIV-D: First Principles (DOI: 10.5281/zenodo.18213618)- XIV-E: Unification (this paper)
Quantum error correction (QEC) relies on redundancy to combat decoherence, yet resource overhead remains the primary barrier to scalability—leading surface-code architectures require O(10³) physical qubits per logical qubit. We propose a complementary approach inspired by Radial Coherential Dynamics (RCD), where decoherence suppression emerges from geometric coupling to a coherential substrate rather than brute isolation. Leveraging the RCD principle that effective coupling strengths scale with √α (where α ≈ 1.3×10⁻⁴ is the universal coherential parameter), we model a "coherential qubit" whose effective dephasing rate is topologically suppressed by √α ≈ 0.0114. Numerical simulation using QuTiP confirms an **87.7× improvement in coherence time** compared to a standard qubit under equivalent environmental coupling. For typical trapped-ion or superconducting qubits with T₂ = 10 μs, RCD predicts **T₂(RCD) ≈ 877 μs**. This constitutes a **falsifiable prediction testable on current hardware platforms**. We present this as a minimal toy model under pure dephasing conditions, intended as an upper-bound estimate rather than a complete QEC protocol. Nevertheless, the results suggest that topological quantum codes (surface codes, color codes) may approximate natural coherential attractors, offering a geometric pathway toward passive fault tolerance with reduced overhead. Framework: Radial Coherential Dynamics (RCD)Author: Arturo Cerezo García (ORCID: 0009-0007-4739-4990)
Radial Coherential Dynamics (RCD) posits a scalar coherence field 𝒞 whose deco- herence drives phenomena from quantum circuit noise to cosmological dark energy. Two mature but disconnected modules exist: (i) a cross-platform analysis of GHZ state fidelity under dephasing-dominated noise, where a Lindblad model with local and col- lective dephasing channels produces a crossover at 𝑁⋆ ≈ 𝛾local/𝛾𝑐; and (ii) a cosmo- logical effective field theory in which a Caldeira–Leggett bath stabilizes a hilltop dark energy potential, with effective coefficients derived from an Ohmic spectral density parametrized by (𝜂, 𝜆, ΛUV). Here we construct a minimal phenomenological bridge between these modules by introducing a single dimensionless parameter 𝜀 ≡ 𝛾𝑐/𝛾local — the fraction of collective-to-local noise — and proposing, as an explicit ansatz, that 𝜀 is approximately scale-invariant. Under this ansatz, the laboratory measurement 𝑁⋆ ≈ 15–20 on IonQ Forte fixes 𝜀 ∈ [0.05, 0.07], which constrains the cosmological bath coupling 𝜂𝜆 to a narrow window. Conversely, the cosmological requirement of controlled backreaction imposes an upper bound 𝜀 < 𝜀max, predicting a lower bound 𝑁⋆ > 1/𝜀max testable in future multi-qubit experiments. For the benchmark param- eters of the HDE series, the three conditions (stabilization, backreaction, and QC data) overlap in the narrow window 𝜀 ∈ [0.05, 0.07], yielding a dark energy equation of state 𝑤0 ≈ −0.987, consistent with current DESI constraints. The bridge is explic- itly falsifiable: non-overlapping 𝜀 windows from QC and cosmology would refute the universal noise ansatz independently of the validity of either module.
This document presents version 1.8 of Radial Coherential Dynamics (RCD), providing computational evidence from real-world datasets across cosmology, quantum decoherence, neural synchronization, and gravitational-wave physics. RCD v1.8 evaluates whether the predictions of the master equation ∂C∂r+2rC+λr(1−C)=0\frac{\partial C}{\partial r} + \frac{2}{r}C + \lambda_r (1 - C) = 0∂r∂C+r2C+λr(1−C)=0 match empirical relaxation, suppression, and coherence patterns observed across more than sixty orders of magnitude. This version includes: Updated measurements of the CMB quadrupole (Planck PR4, Cea 2022, Herold 2025). Decoherence times from superconducting cavities (Weizmann 2023; Reagor et al. 2016). Neural synchronization thresholds (HCP, meditation, anesthesia, psychedelic states). Gravitational-wave ringdown values from GW150914. A statistical analysis showing multi-domain agreement with RCD predictions. Reproducible Python code for fitting, regression, and parameter extraction. RCD v1.8 is published under a non-commercial, open-science ethos, with complete transparency and reproducibility. All numerical values and comparisons are derived from publicly available data.
This work develops the conceptual and physical foundations of emergent causality and time within the framework of Radial Coherential Dynamics (RCD). It explores how relativistic structure, causal order, and effective temporal dynamics arise from a coherence-based description of quantum systems, emphasizing the role of decoherence, entanglement structure, and information flow. The document is intended as a theoretical monograph within the broader RCD research program, bridging foundational concepts and future experimental validation, without presupposing a fixed publication sequence.