Quantum kernel-based delta (Δ)-learning for correcting a semiempirical method in the prediction of reaction barrier heights

Abstract

A quantum machine learning based Δ-learning framework is presented for the prediction of reaction barrier heights of organic molecules. Corrections learned by quantum kernel-based models are applied to mitigate the underlying errors of the semiempirical PM7 method, improving its predictive accuracy toward results obtained at the ωB97X-D3/def2-TZVP level of theory. Both fidelity and projected quantum kernels are implemented using seven distinct encoding circuits and passed to three classical regression algorithms, namely, support vector regression, kernel ridge regression, and Gaussian process regression, yielding a total of 840 benchmarked model configurations across circuit widths of up to 9 qubits and circuit depths of up to five layer repetitions. The encoding circuits are additionally characterized in terms of their expressibility and entangling capability. The top-performing models, constructed using the 9-qubit YZ-CX encoding circuit, predict reaction barrier heights with a mean absolute error ranging between 4.95 and 5.03 kcal/mol, underscoring an improvement of ∼54% over the uncorrected PM7 baseline.