Quantum Annealing (QA) is a quantum computing paradigm for solving combinatorial optimization problems formulated as Quadratic Unconstrained Binary Optimization (QUBO) problems. An essential step in QA is minor embedding, which maps the problem graph onto the sparse topology of the quantum processor. This process is computationally expensive and scales poorly with increasing problem size and hardware complexity. Existing heuristics are often developed for specific problem graphs or hardware topologies and are difficult to generalize. Reinforcement Learning (RL) offers a promising alternative by treating minor embedding as a sequential decision-making problem, where an agent learns to construct minor embeddings by iteratively mapping the problem variables to the hardware qubits. We propose a RL-based approach to minor embedding using a Proximal Policy Optimization agent, testing its ability to embed both fully connected and randomly generated problem graphs on two hardware topologies, Chimera and Zephyr. The results show that our agent consistently produces valid minor embeddings, with reasonably efficient number of qubits, in particular on the more modern Zephyr topology. Our proposed approach is also able to scale to moderate problem sizes and adapts well to different graph structures, highlighting RL's potential as a flexible and general-purpose framework for minor embedding in QA.

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.