Exploratory Benchmark — Applied Quantum Computing Track This record presents an exploratory optimization 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 applications to variational quantum eigensolvers on molecular and lattice systems, this work explores the transfer of a fixed decoherence regulation law to a quantum optimization algorithm. The Quantum Approximate Optimization Algorithm (QAOA) is applied to the MaxCut problem on a fixed graph. Performance is evaluated using the approximation ratio and the gap to the optimal solution as primary metrics. A controlled A/B methodology is employed: identical QAOA circuits 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 or algorithmic modifications are introduced. The results show a consistent improvement in optimization performance, with an average increase in approximation ratio of approximately 9–10% and a reduction of the optimization gap of approximately 25%, with the effect becoming more pronounced at higher circuit depths. This benchmark does not claim algorithmic optimality or quantum advantage. Its purpose is to assess whether a decoherence suppression law—originally derived for single-qubit dynamics—produces consistent and transferable effects when applied, without tuning, to variational quantum optimization algorithms. All code, data, and figures are provided for independent evaluation by the scientific community.
Exploratory Benchmark — Applied Quantum Computing Track This record presents an exploratory optimization 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 applications to variational quantum eigensolvers on molecular and lattice systems, this work explores the transfer of a fixed decoherence regulation law to a quantum optimization algorithm. The Quantum Approximate Optimization Algorithm (QAOA) is applied to the MaxCut problem on a fixed graph. Performance is evaluated using the approximation ratio and the gap to the optimal solution as primary metrics. A controlled A/B methodology is employed: identical QAOA circuits 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 or algorithmic modifications are introduced. The results show a consistent improvement in optimization performance, with an average increase in approximation ratio of approximately 9–10% and a reduction of the optimization gap of approximately 25%, with the effect becoming more pronounced at higher circuit depths. This benchmark does not claim algorithmic optimality or quantum advantage. Its purpose is to assess whether a decoherence suppression law—originally derived for single-qubit dynamics—produces consistent and transferable effects when applied, without tuning, to variational quantum optimization algorithms. All code, data, and figures are provided for independent evaluation by the scientific community.
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.
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.”
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.
Exploratory Benchmark — Applied Quantum Computing Track This record presents an exploratory 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 first algorithmic application (Coherence-Regulated Variational Quantum Eigensolver: An Exploratory H₄ Benchmark, Zenodo, December 2025, DOI: 10.5281/zenodo.18049302), this work explores the impact of a fixed decoherence regulation law on variational quantum algorithms applied to a graphene-inspired system. An effective six-site graphene hexagon is modeled using a Fermi–Hubbard Hamiltonian with periodic boundary conditions. Variational Quantum Eigensolver (VQE) simulations are performed for both the neutral (N = 6) and hole-doped (N = 5) cases over 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 scaled according to the previously published law T2→T2/αT_2 \rightarrow T_2/\sqrt{\alpha}T2→T2/α with fixed α≈1.3×10−4\alpha \approx 1.3 \times 10^{-4}α≈1.3×10−4. No additional parameters are introduced. This work does not claim ab initio graphene results. The “exact” reference corresponds to the ground state of the effective Hubbard model used here. The benchmark is intended solely to assess whether a previously established decoherence suppression law produces consistent effects when transferred, without tuning, to multi-qubit variational algorithms. All code, data, and figures are provided for independent evaluation by the scientific community.
The Quantum Approximate Optimization Algorithm (QAOA) is a hybrid quantum-classical algorithm to solve binary-variable optimization problems. Due to its expected robustness to systematic errors and the short circuit depth, it is one of the promising candidates likely to run on near-term quantum devices. We project the performance of QAOA applied to the Max-Cut problem and compare it with some of the best classical alternatives, both for exact or approximate solution. When comparing approximate solvers, their performance is characterized by the computational time taken to achieve a given quality of solution. Since QAOA is based on sampling, we introduce performance metrics based on the probability of observing a sample above a certain quality. In addition, we show that the QAOA performance varies significantly with the graph type. By selecting a suitable optimizer for the variational parameters and reducing the number of function evaluations, QAOA performance improves by up to 2 orders of magnitude compared to previous estimates. Especially for 3-regular random graphs, this setting decreases the performance gap with classical alternatives.
Variational quantum optimization provides a useful setting for examining how circuit structure, parameterization, and trainability interact in practice. Objectives: Among the most promising variational quantum algorithms, the Quantum Approximate Optimization Algorithm (QAOA) depends critically on circuit architecture, but greater circuit complexity does not necessarily lead to easier optimization or better solutions. Using the Maximum Cut (MaxCut) problem on graphs as a controlled setting, we investigate how variational behavior changes as problem-specific QAOA structure is progressively removed, with particular attention to representational capacity, optimization geometry, and finite-budget trainability. Methods: We analytically characterize a graph-agnostic product-state formulation of MaxCut and derive exact equivalences, redundancies, and local-landscape properties. These results motivate a controlled comparison among separable product ansätze, a representative graphagnostic entangling circuit, and graph-structured QAOA at several depths, including a parameter-count-matched control. The numerical benchmark comprises 95 small unweighted graph instances optimized under a common objective-evaluation budget. Results: The product-state formulation preserves the exact discrete MaxCut optimum, while its strict local maxima correspond to classical cuts that are stable under singlevertex flips. Redundant phase parameters increase optimization effort without enlarging the objective-relevant family. Under the prescribed optimization budget, the productstate ansatz attains higher average solution quality than the tested QAOA depths while requiring substantially fewer objective evaluations. The graph-agnostic entangling comparator provides no consistent advantage over the separable baseline, and a simple classical local-search method remains highly competitive. Conclusion: In the regime considered here, objective-relevant parameterization and optimization geometry can be as important as circuit richness.