Hardware‐Efficient Ansatz Variational Quantum Regression for Molecular Energy Prediction

ABSTRACT We propose a variational quantum regression (VQR) algorithm using a hardware‐efficient ansatz (HEA) structure. This approach enables the quantum state to directly encode classical tabular data with variational parameters corresponding to real‐valued regression coefficients, ensuring high interpretability and efficient optimization without sacrificing expressiveness. By combining a variational quantum circuit with a classical optimizer, our method predicts the ground‐state energy of a hydrogen molecule using full configuration interaction (FCI) data. We quantify the expressibility of the VQR HEA circuit via the Kullback–Leibler (KL) divergence D KL and show the advantages of our R y − R x gate sequence in balancing expressibility. Performed for pennylane using an idealized quantum simulator, our 4‐qubit, 5‐layer HEA‐based VQR model achieves an accuracy of ∼0.99, mean squared error (MSE) < 10 −6 Hartree 2 , and mean absolute error (MAE) around 0.1 × 10 −2 Hartree compared to FCI benchmarks. We further demonstrate how qubit number and layer depth influence model accuracy, providing insights for task‐specific quantum circuit design. Our results advance practical applications of quantum computing for electronic structure problems by introducing an expressive, interpretable ansatz tailored for high‐precision simulations.