Coherence-Regulated VQE for a Graphene Hexagon: An Exploratory Hubbard-Model Benchmark Based on a Published Decoherence Law

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.