Generalization of the decomposition selector to broader graph families

Establish whether the learned selector for choosing between the Pauli and matching Hamiltonian decompositions generalizes to continuous-time quantum walks on graph classes beyond the eight-vertex exhaustive population and the two tested source families, particularly graph families commonly used in continuous-time quantum-walk search problems.

Background

The study trains and evaluates its selector primarily on the complete population of connected eight-vertex graphs, then tests transfer on larger graphs drawn from Erdős–Rényi and structured graph families. Because these two larger-graph families are strongly associated with different decomposition winners, successful transfer between them does not establish generalization to arbitrary graph distributions.

The authors explicitly identify evaluation on additional graph families as necessary to determine whether the learned decision boundary is universal or instead specific to the families used in the transfer test. This is particularly relevant for graph families arising in continuous-time quantum-walk search problems, which were not evaluated.