Integrated error-suppressed pipeline for quantum optimization of nontrivial binary combinatorial optimization problems on gate-model hardware at the 156-qubit scale

We introduce a novel hybrid quantum-classical variational optimization method for unconstrained binary combinatorial optimization problems on gate-model quantum computers, integrating a custom variational ansatz, staged feedback-based dual variational parameter update strategies, efficient parametric compilation, automated error suppression during hardware execution, and scalable O($n$) classical post-processing to correct for bitflip errors. Without this integrated approach, we show that standard circuit execution at scale produces output indistinguishable from random sampling, establishing the necessity of each pipeline component. We benchmark the method on IBM superconducting quantum computers for classically nontrivial optimization problems, where the optimization is conducted on hardware with no use of classical simulation or prior knowledge of the solution. For Max-Cut on random regular graphs with topologies not matched to device connectivity, the method achieves approximation ratios of 100% for unweighted 3-regular graphs up to 156 nodes, weighted regular graphs up to 80 nodes, and weighted 7-regular graphs up 50 nodes. Applied to higher-order binary optimization, the method finds the ground state energy of 127- and 156-qubit spin-glass models matched to device topology with linear, quadratic, and cubic interaction terms, achieving approximation ratios of at least 99.5% across all instances tested. The method consistently outperforms a classical local solver across all problems. Where published results on identical problem instances are available, our method demonstrates competitive or superior performance. These results demonstrate that an appropriately engineered approach enables gate-model quantum computers to produce high-quality solutions for nontrivial binary optimization problems at the 156 qubit scale, where naive implementations are insufficient for good performance.