Embedding-Aware Noise Modeling of Quantum Annealing
Seon-Geun Jeong, Mai Dinh Cong, Dae-Il Noh, Quoc-Viet Pham, Won-Joo Hwang
TL;DR
This work tackles the scalability challenges of quantum annealing arising from embedding overhead in sparse hardware by introducing an embedding-aware noise model that extends the integrated control error framework with Gaussian chain-level errors. It derives closed-form scaling relations for chain-break probability and chain-break fraction as functions of embedding size and validates them through experiments on D-Wave's Zephyr topology, demonstrating a practical design rule that chain strength should grow roughly as $\sqrt{\ell_i}$ to preserve reliability. The results reveal a sublinear but steeper-than-ideal scaling due to correlated hardware noise, prompting refinements to the model and highlighting embedding-aware calibration as essential for large-scale QA. The framework provides predictive tools for scalability assessment, guiding embedding-aware parameter tuning and hardware-conscious noise modeling toward more reliable quantum annealing on current devices.
Abstract
Quantum annealing provides a practical realization of adiabatic quantum computation and has emerged as a promising approach for solving large-scale combinatorial optimization problems. However, current devices remain constrained by sparse hardware connectivity, which requires embedding logical variables into chains of physical qubits. This embedding overhead limits scalability and reduces reliability as longer chains are more prone to noise-induced errors. In this work, building on the known structural result that the average chain length in clique embeddings grows linearly with the problem size, we develop a mathematical framework that connects embedding-induced overhead with hardware noise in D-Wave's Zephyr topology. Our analysis derives closed-form expressions for chain break probability and chain break fraction under a Gaussian control error model, establishing how noise scales with embedding size and how chain strength should be adjusted with chain length to maintain reliability. Experimental results from the Zephyr topology-based quantum processing unit confirm the accuracy of these predictions, demonstrating both the validity of the theoretical noise model and the practical relevance of the derived scaling rule. Beyond validating a theoretical model against hardware data, our findings establish a general embedding-aware noise framework that explains the trade-off between chain stability and logical coupler fidelity. Our framework advances the understanding of noise amplification in current devices and provides quantitative guidance for embedding-aware parameter tuning strategies.