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arXiv · 2504.02340

Perturbative Variational Quantum Eigensolver via Reduced Density Matrices

Yuhan Zheng·Yibin Guo·Huili Zhang·Jie Liu·Xiongzhi Zeng·Xiaoxia Cai·Zhenyu Li·Jinlong Yang
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Abstract

Current noisy intermediate-scale quantum (NISQ) devices remain limited in their ability to perform accurate quantum chemistry simulations due to restricted numbers of high-fidelity qubits and short coherence times. To overcome these challenges, we introduce a reduced density matrix (RDM)-based perturbative variational quantum eigensolver (VQE) framework that augments active-space VQE with perturbation theory to recover electron correlation beyond the active space without increasing the qubit count or variational circuit depth. We formulate a fully coupled approach (VQE-PTs) and a diagonal approximation (VQE-PT). The former retains couplings among orthonormalized perturbers, whereas the latter neglects these couplings to simplify the classical post-processing. Numerical simulations of HF, N$_2$, and F$_2$ show that VQE-PTs provides a robust formulation across different molecular systems, while VQE-PT offers an efficient approximation. We further experimentally implement VQE-PT on the Quafu superconducting quantum processor for F$_2$, achieving a mean absolute error of 1.2 millihartree along the potential energy surface after error mitigation. These results demonstrate perturbative VQE as a practical framework for incorporating dynamic correlation in quantum chemistry simulations.

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Yuhan Zheng, Yibin Guo, Huili Zhang, Jie Liu, Xiongzhi Zeng, Xiaoxia Cai, Zhenyu Li, Jinlong Yang. 2025-04-03. Perturbative Variational Quantum Eigensolver via Reduced Density Matrices. https://arxiv.org/abs/2504.02340

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