Relational Quantum Ground State Prediction: A Green AI Approach to the 2D Transverse Field Ising Model

Simulating quantum many-body ground states is constrained by the exponential scaling of the Hilbert space. Recent approaches rely on massive, parameter-heavy neural networks and resource-intensive Variational Monte Carlo (VMC) techniques. We compare two paradigms applied to the 2D Transverse Field Ising Model (TFIM) on an 8,100-qubit unfrustrated square lattice: Hamilton-Zero (a 547-million parameter foundation model) and ODSA 1 (Ontometric Dual Stream Architecture, a proprietary ML design pattern and hyper-compact graph-topological surrogate with ~154,000 parameters). The ODSA architecture leverages relational calculus and a 1/N fractional mass term to enable scale-invariant zero-shot extrapolation from micro-cluster training. It achieves 0.7% error against the exact thermodynamic limit (-2.03129) in 83 milliseconds on a standard CPU. In contrast, under zero-shot evaluation at 8,100 qubits on its own large-system benchmark, Hamilton-Zero produces an unphysical positive energy (+0.128, against a reference near −0.50), and no fine-tuned result at that scale is reported. On 100 disordered spin glass instances, ODSA evaluates each in 93 milliseconds — a speedup of approximately 400 hours against equivalent VMC. We conclude that mathematical reframing via relational topology dramatically outperforms brute-force parameter scaling, achieving deterministic physical convergence with a fraction of the carbon and hardware footprint.