  This paper introduces a novel quantum embedding search algorithm (QES,
pronounced as "quest"), enabling search for optimal quantum embedding design
for a specific dataset of interest. First, we establish the connection between
the structures of quantum embedding and the representations of directed
multi-graphs, enabling a well-defined search space. Second, we instigate the
entanglement level to reduce the cardinality of the search space to a feasible
size for practical implementations. Finally, we mitigate the cost of evaluating
the true loss function by using surrogate models via sequential model-based
optimization. We demonstrate the feasibility of our proposed approach on
synthesis and Iris datasets, which empirically shows that found quantum
embedding architecture by QES outperforms manual designs whereas achieving
comparable performance to classical machine learning models.
