Minor Embedding for Max-Cut: Empirical Analysis of Quantum Annealing’s Combinatorial Bottleneck
Year: 2026
Type: conference-paper
Abstract: Quantum optimization by annealing constitutes a stochastic global search over QUBO-formulated combinatorial optimization problems. Its performance depends on pre-solving the Minor Embedding (ME) challenge—the $\mathcal{N}\mathcal{P}$-hard problem of mapping logical graphs representing QUBOs onto the quantum hardware. Despite determining solution feasibility and quality, ME remains understudied as a standalone optimization challenge. Current understanding is largely limited to synthetic graphs on isolated topologies, leaving the generalizability of structural predictors across hardware generations unclear. We conduct the first cross-topology study analyzing the MINORMINER heuristic—the de facto industry standard—over ≈550 benchmark graph instances across D-Wave’s Chimera, Pegasus, and Zephyr architectures. Our analyses reveal a functional dissociation between embedding feasibility and cost: topological independence (via Maximum Independent Set ratio) predicts feasibility by identifying structural ‘slack’, while edge density—reflecting clique-like proximity—governs the resource ‘toll’ (chain length). Since ME is a purely graph-theoretic problem, agnostic to the combinatorial origin of the source graph, these structural predictors apply to any QUBO whose logical graph falls within the studied structural regime. This dissociation remains invariant across all architectures, establishing ME as a benchmark for Evolutionary Computation, where the local distribution of edges, rather than global density alone, determines algorithmic difficulty.
Authors: Ron Lavi, Alberto Moraglio, Ofer M. Shir
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W7224020509