Toward Accurate Post-Born-Oppenheimer Molecular Simulations on Quantum Computers: An Adaptive Variational Eigensolver with Nuclear-Electronic Frozen Natural Orbitals

TL;DR

This paper introduces an adaptive variational quantum algorithm for nuclear-electronic orbital simulations that significantly reduces quantum resource requirements, enabling more practical non-Born--Oppenheimer molecular simulations on near-term quantum computers.

Contribution

It extends the ADAPT-VQE method to the NEO framework using frozen natural orbitals, achieving large reductions in CNOT gates while maintaining accuracy.

Findings

Reduces CNOT count by several orders of magnitude compared to NEO-UCCSD.

Successfully captures isotope effects and improves zero-point energy predictions.

Demonstrates feasibility of NEO simulations on near-term quantum devices.

Abstract

Nuclear quantum effects such as zero-point energy and hydrogen tunnelling play a central role in many biological and chemical processes. The nuclear-electronic orbital (NEO) approach captures these effects by treating selected nuclei quantum mechanically on the same footing as electrons. On classical computers, the resources required for an exact solution of NEO-based models grow exponentially with system size. By contrast, quantum computers offer a means of solving this problem with polynomial scaling. However, due to the limitations of current quantum devices, NEO simulations are confined to the smallest systems described by minimal basis sets whereas realistic simulations beyond the Born--Oppenheimer approximation require more sophisticated basis sets. For this purpose, we herein extend a hardware-efficient ADAPT-VQE method to the NEO framework in the frozen natural orbital (FNO) basis. We demonstrate on H$_2$ and D$_2$ molecules that the NEO-FNO-ADAPT-VQE method reduces the CNOT count by a several orders of magnitude relative to the NEO unitary coupled cluster method with singles and doubles (NEO-UCCSD) while maintaining the desired accuracy. This extreme reduction in the CNOT gate count is sufficient to permit practical computations employing the NEO method -- an important step toward accurate simulations involving non-classical nuclei and non--Born--Oppenheimer effects on near-term quantum devices. We further show that the method can capture isotope effects and we demonstrate that inclusion of correlation energy systematically improves the prediction of $\Delta$ZPE.