Embedding-aware noise modeling of quantum annealing

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, we develop an embedding-aware baseline noise framework that connects chain-length growth to accumulated integrated-control-error variance, chain break probability (CBP), chain break fraction (CBF), and chain-strength scaling. We distinguish a moment-level uncorrelated ICE baseline, which yields a linear variance law, from a Gaussian closure that gives a closed-form erfc approximation for CBP. Experiments on the D-Wave Advantage2 Zephyr processor show that the calibrated baseline model captures the dominant growth trend of CBF with embedding size. However, the empirical critical chain-strength exponent ranges from $$\alpha =0.805$$ to $$\alpha =1.006$$ across chain-break tolerance thresholds, with 95% bootstrap confidence intervals consistently excluding the independent-noise prediction $$\alpha =0.5$$ ; a direct fit of a correlated-variance extension recovers $$\gamma \approx 1.8$$ , consistent with the asymptotic relation $$\gamma =2\alpha $$ . These results indicate that real-hardware variance accumulation deviates from the independent-noise reference and is consistent with a correlated component. The proposed framework offers quantitative guidance for embedding-aware chain-strength tuning and motivates more general noise models incorporating correlated and non-Gaussian hardware effects.