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RCD Paper XIII: From Field to Hamiltonian — Formalizing the RCD C-Field as Quantum Protection Operator

Arturo Cerezo, IA Collaborative Panel — Claude (Anthropic) • ChatGPT (OpenAI) • Gemini (Google) • Grok (xAI)

Published Jan 8, 2026• 0 citations
Publisher

Abstract

Paper XII established mathematical isomorphisms between the RCD coherence field C and four quantum protection mechanisms. This paper advances from functional correspondence to operational formalization, deriving an explicit mapping C(x,t) → H_prot that translates the abstract functional role of the coherence field into concrete quantum operators. We show that the C-field naturally generates a protection Hamiltonian of the general form H_prot = f(C) · O_sys, where f(C) is a monotonic function of local coherence and its derivatives, and O_sys is a system-dependent operator. This unified form encompasses Zeno coupling, topological gap protection, dynamical decoupling, and frustration-based suppression. The mapping f(C) is not unique; different physical platforms may realize equivalent protection through distinct microscopic implementations. Recent experimental results, including Google Quantum AI's surface code performance, provide illustrative calibration examples linking RCD parameters to measurable protection strengths. The formalization enables, in principle, quantitative predictions for experimental tests of RCD in engineered quantum systems. This is Paper XIII in the RCD series, completing the Quantum Binding track initiated in Papers XI-XII. Keywords: coherence field, protection Hamiltonian, quantum operators, RCD theory, decoherence suppression, dynamic rigidity, operator formalism, Hamiltonian mapping, Radial Coherential Dynamics

DOI
10.5281/zenodo.18180117

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Paper XII established mathematical isomorphisms between the RCD coherence field C and four quantum protection mechanisms. This paper advances from functional correspondence to operational formalization, deriving an explicit mapping C(x,t) → H_prot that translates the abstract functional role of the coherence field into concrete quantum operators. We show that the C-field naturally generates a protection Hamiltonian of the general form H_prot = f(C) · O_sys, where f(C) is a monotonic function of local coherence and its derivatives, and O_sys is a system-dependent operator. This unified form encompasses Zeno coupling, topological gap protection, dynamical decoupling, and frustration-based suppression. The mapping f(C) is not unique; different physical platforms may realize equivalent protection through distinct microscopic implementations. Recent experimental results, including Google Quantum AI's surface code performance, provide illustrative calibration examples linking RCD parameters to measurable protection strengths. The formalization enables, in principle, quantitative predictions for experimental tests of RCD in engineered quantum systems. This is Paper XIII in the RCD series, completing the Quantum Binding track initiated in Papers XI-XII. Keywords: coherence field, protection Hamiltonian, quantum operators, RCD theory, decoherence suppression, dynamic rigidity, operator formalism, Hamiltonian mapping, Radial Coherential Dynamics
We establish formal mathematical isomorphisms between the coherence field C proposed in Radial Coherential Dynamics (RCD) and four established quantum protection mechanisms: continuous quantum Zeno effect, topological energy gaps, continuous dynamical decoupling (CDD), and thermodynamic frustration of decoherence. Our results demonstrate that unprotected quantum entanglement collapses faster than classical schemes under realistic noise, and that only architectures incorporating a dynamic rigidity mechanism — isomorphic to continuous Zeno, topological gaps, or decoherence frustration — can surpass the classical binding limit. Recent experimental validations, including Google Quantum AI's surface code achieving error suppression factor Λ = 2.14 and JILA's Zeno suppression in ultracold KRb molecules, provide empirical grounding for these theoretical correspondences. We demonstrate that the mathematical role played by the RCD C-field is isomorphic to that realized by several established coherence-protection mechanisms, suggesting a common functional role across diverse physical implementations. This is Paper XII in the RCD series, continuing the Quantum Binding track initiated in Paper XI. Keywords: coherence protection, quantum Zeno effect, topological protection, decoherence-free subspaces, quantum error correction, RCD theory, binding problem, isomorphism, Radial Coherential Dynamics
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)
Exploratory Benchmark — Applied Quantum Computing Track This record presents the first applied benchmark in the quantum computing track of the Radial Coherential Dynamics (RCD) research program. Building upon the previously published decoherence suppression model (Topological Decoherence Suppression via Coherential Geometry, Zenodo, December 2025, DOI: 10.5281/zenodo.18000641), which predicts a √α reduction of effective dephasing rates (α ≈ 1.3×10⁻⁴), this work explores the implications of that fixed decoherence law for variational quantum algorithms operating under noisy conditions. As an exploratory benchmark, the RCD noise suppression law (γ₍RCD₎ = γ₀√α) is applied to a Variational Quantum Eigensolver (VQE) simulation targeting the H₄ molecule in rectangular geometry. A controlled A/B methodology is employed: identical VQE simulations are performed using standard noise parameters (control) and RCD-regulated noise parameters (treatment), with all Hamiltonian, ansatz, optimizer, and geometry settings held fixed. This work does not claim molecular validation of RCD. Rather, it investigates whether a decoherence suppression law—previously established for single-qubit dynamics—produces observable effects when transferred, without additional tuning, to multi-qubit variational algorithms. All code, data, and figures are provided for independent evaluation by the scientific community. Guiding principle: “We do not use quantum computing as an oracle, but as a controlled laboratory of coherence.”
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.
This preprint presents Temporal Decoherence Theory (TDT), the v16 extension of Radial Coherential Dynamics (RCD), offering a complete solution to the problem of time in physics. We propose that time does not exist as a fundamental dimension; instead, time is defined as the rate at which coherence decays in the universal coherence field C(x,t)C(x,t)C(x,t). The central result is the emergent-time equation: dt=−dCΓdt = -\frac{dC}{\Gamma}dt=−ΓdC where Γ\GammaΓ is the decoherence rate.This single relation unifies thermodynamics, causality, relativity, quantum mechanics, and cosmology under one coherent framework. Key results include: The arrow of time emerges automatically from monotonic coherence decay. The Second Law of Thermodynamics is derived rather than postulated: entropy increases because dC<0dC < 0dC<0. Causality is coherence ordering: higher coherence states cause lower coherence states. Relativistic time dilation (gravitational and kinematic) arises from variations in the local coherence field. Schrödinger’s equation is derived from coherence evolution. The age and structure of the universe follow from cumulative decoherence since C=1C = 1C=1 at the Big Bang. RCD v16 completes the conceptual unification of the theory: space, time, matter, gauge fields, quantum behavior, and gravity all emerge from the dynamics of a single coherence field. This release establishes the foundation for RCD v17, which will present the full Lagrangian and complete mathematical unification.