  Quantum Annealing (QA) holds great potential for solving combinatorial
optimization problems efficiently. However, the effectiveness of QA algorithms
heavily relies on the embedding of problem instances, represented as logical
graphs, into the quantum unit processing (QPU) whose topology is in form of a
limited connectivity graph, known as the minor embedding Problem. Existing
methods for the minor embedding problem suffer from scalability issues when
confronted with larger problem sizes. In this paper, we propose a novel
approach utilizing Reinforcement Learning (RL) techniques to address the minor
embedding problem, named CHARME. CHARME includes three key components: a Graph
Neural Network (GNN) architecture for policy modeling, a state transition
algorithm ensuring solution validity, and an order exploration strategy for
effective training. Through comprehensive experiments on synthetic and
real-world instances, we demonstrate that the efficiency of our proposed order
exploration strategy as well as our proposed RL framework, CHARME. In details,
CHARME yields superior solutions compared to fast embedding methods such as
Minorminer and ATOM. Moreover, our method surpasses the OCT-based approach,
known for its slower runtime but high-quality solutions, in several cases. In
addition, our proposed exploration enhances the efficiency of the training of
the CHARME framework by providing better solutions compared to the greedy
strategy.
