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)
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.”
Exploratory Benchmark — Applied Quantum Computing Track This record presents the third variational-algorithm benchmark in the applied 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), and its prior algorithmic benchmarks on molecular and two-dimensional lattice systems, this work explores the transfer of a fixed decoherence regulation law to a one-dimensional correlated system with open boundaries. An eight-site one-dimensional Hubbard chain with open boundary conditions (OBC) is simulated using the Variational Quantum Eigensolver (VQE). Ground-state energies, energy errors, and charge-density (Friedel) oscillations are evaluated across a range of interaction strengths U/t. A controlled A/B methodology is employed: identical VQE simulations are executed using standard noise parameters (control) and RCD-regulated noise parameters (treatment), where the dephasing time is rescaled according to the previously published lawT₂ → T₂ / √α, with fixed α ≈ 1.3 × 10⁻⁴. No additional parameters are introduced. The results show a consistent reduction of VQE energy error of approximately 40–45% across weak, intermediate, and strongly correlated regimes, including the Mott-transition region. Spatial observables indicate improved preservation of correlation-induced structure under coherence regulation. This benchmark does not claim ab initio condensed-matter results. Its purpose is to assess whether a decoherence suppression law—originally derived for single-qubit dynamics—produces consistent and topology-independent effects when transferred, without tuning, to multi-qubit variational algorithms. All code, data, and figures are provided for independent evaluation by the scientific community.
Quantum error correction (QEC) represents a critical enabler for fault-tolerant quantum computing, protecting fragile quantum states from decoherence and operational errors. This paper provides a comprehensive analysis of leading quantum error correction schemes, focusing on surface codes and topological codes within the context of Noisy Intermediate-Scale Quantum (NISQ) era processors. We examine the theoretical foundations of stabilizer codes, compare surface code implementations with code distances ranging from d=3 to d=17, and analyze topological codes including toric codes and color codes. Our investigation encompasses syndrome extraction circuits, logical qubit encoding strategies, and threshold analysis for contemporary quantum hardware platforms. Performance metrics reveal that surface codes achieve error thresholds of approximately 1% with realistic noise models, while topological codes offer architectural advantages for specific qubit connectivity constraints. We discuss implementation challenges on current NISQ processors including IBM Quantum, Google Sycamore, and IonQ systems, addressing qubit overhead, gate fidelity requirements, and decoding algorithms. This analysis provides insights for selecting appropriate error correction schemes based on application requirements and hardware capabilities.
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
The global pursuit of fault-tolerant quantum computing is fundamentally bottlenecked by environmentally induced decoherence. Current scaling models rely on Quantum Error Correction (QEC) surface and toric codes, assuming that continuous physical qubit scaling can outpace localized decoherence rates. This probabilistic assumption lacks a deterministic, geometric boundary for multi-qubit entanglement collapse. This paper introduces a strict, deterministic topo-dynamical framework for quantum array scaling. By modeling the macroscopic quantum state as a structural competition between the spatial propagation of entanglement coherence and localized environmental decay, we derive a universal square-root geometric invariant (ℓdec). We mathematically demonstrate that this invariant defines the absolute maximum spatial footprint an entangled array can occupy before environmental noise forces an irreversible transition into a classical statistical mixture. Furthermore, we provide concrete scaling examples utilizing contemporary T1/T2 values, outlining experimental validation protocols for existing superconducting processors and providing a deterministic blueprint for active noise control and topological isolation.
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.