Minor Embedding for Quantum Annealing with Reinforcement Learning

2025-07-21

AI Summary

Computing minor embeddings of problem graphs onto sparse hardware topologies (e.g., Chimera, Zephyr) for quantum annealing is computationally expensive, poorly generalizable, and inherently unscalable. Method: We propose the first reinforcement learning–based general embedding framework, modeling embedding as a sequential decision-making process. Our approach employs Proximal Policy Optimization (PPO), augmented with graph neural networks and structure-aware state encoding, to adaptively map heterogeneous problem graphs onto novel hardware topologies. Contribution/Results: The framework achieves the first efficient minor embedding on modern topologies such as Zephyr, significantly reducing physical qubit overhead. It exhibits strong generalization—trained policies transfer across diverse problem classes and hardware architectures—eliminating structural dependencies inherent in traditional heuristic methods. By decoupling embedding from topology-specific hand-crafted rules, our method establishes a scalable, learning-driven paradigm for quantum annealing applications.

Technology Category

• Search and Optimization: Learning to Search
• Machine Learning: Quantum Machine Learning
• Planning, Routing, and Scheduling: Learning for Planning and Scheduling

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

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.

Problem

• Efficiently map QUBO problems to quantum hardware
• Overcome scalability issues in minor embedding
• Generalize embedding across diverse graph topologies

Innovation

• Reinforcement Learning for minor embedding
• Proximal Policy Optimization agent approach
• Adapts to various graph and hardware topologies