Experimental Workflows for Combinatorial Optimization: Towards Quantum Advantage

TL;DR

This paper introduces a sandbox platform for hybrid quantum-classical workflows in graph optimization, demonstrating end-to-end experiments on IBM quantum hardware to assess quantum advantage in combinatorial problems.

Contribution

It presents a practical workflow integrating classical preprocessing, quantum optimization, and classical postprocessing for combinatorial problems, with real hardware experiments on large graphs.

Findings

Successfully solved graphs up to 128 vertices on IBM quantum hardware.

Identified bottlenecks and workload partitioning strategies in quantum optimization.

Provided a practical guide for interpreting quantum optimization results.

Abstract

Demonstrating quantum advantage for combinatorial optimization requires more than standalone algorithmic results; it calls for end-to-end case studies that integrate problem modelling, quantum execution, and classical refinement into practical workflows. This paper presents a sandbox platform for experimenting with hybrid quantum-classical workflows in graph optimization, enabling the systematic study of end-to-end optimization pipelines. Using our platform, we investigate three classically intractable and mutually reducible graph problems -- Minimum Vertex Cover, Maximum Independent Set, and Maximum Clique -- by transforming them into an unconstrained problem and solving the resulting instances with QAOA on IBM platforms. Our workflow combines classical pre-processing to reduce instance size, quantum optimization on the reduced problem, and classical postprocessing to map quantum outputs to high-quality feasible solutions, thereby avoiding direct constraint encoding in the quantum circuit. We evaluate the approach on synthetic graphs, benchmark instances, and real-world networks, and report hardware experiments on IBM Quantum System One at PINQ2 in Bromont, Quebec, powered by IBM's 156-qubit Heron r2 processor on graphs up to 128 vertices, with circuits involving up to 128 qubits and 13,555 two-qubit gates. The results illustrate how sandbox-style end-to-end experimentation can expose bottlenecks, clarify the role of classical-quantum workload partitioning, and provide domain experts and practitioners with a practical guide for interpreting quantum optimization outputs and assessing quantum utility on the road to quantum advantage in combinatorial optimization.