Topology-Aware Robustness Prediction: K-Hop Entropy Analysis of D-Wave Zephyr Architectures

The physical connectivity of quantum processors significantly affects the performance and robustness of embedded quantum algorithms, particularly in architectures like D-Wave’s Zephyr. This work examines the use of K-hop Entropy Metric (KHEM) as a topology-aware metric to predict the stability of logical-to-physical qubit embeddings, eliminating the need for explicit noise models. KHEM quantifies the degree of heterogeneity within the k-hop neighborhood of each node. This provides insights into the local structural variability that influences the length of the embedding chain and the physical separation of the logical qubits. The present study analyzed simulated embeddings of Erdos–Renyi (ER) and complete logical graphs onto a Zephyr-8 architecture to assess the relationship between KHEM, average chain length, and hop-distance distributions. Jensen–Shannon Divergence (JSD) was then used to compare k = 2 and k = 3 distributions, while KHEM was shown to provide a fast, topology-driven pre-filter for robustness estimation on Zephyr-8.