Minor Embedding for Quantum Annealing with Reinforcement Learning

TL;DR

This paper introduces a reinforcement learning method using Proximal Policy Optimization to automate and improve the process of minor embedding in quantum annealing, demonstrating adaptability and efficiency across different graph types and hardware topologies.

Contribution

It presents the first RL-based approach for minor embedding in quantum annealing, capable of generalizing across various problem graphs and hardware configurations.

Findings

RL agent consistently produces valid embeddings

Efficient embedding on modern Zephyr topology

Scales to moderate problem sizes and adapts to different graphs

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.