A Quantum Computing Implementation of Nuclear-Electronic Orbital (NEO) Theory: Towards an Exact pre-Born-Oppenheimer Formulation of Molecular Quantum Systems

TL;DR

This paper presents a quantum computing approach for accurately simulating coupled electron-nuclear systems in molecules, reducing resource needs while achieving benchmark-level accuracy for ground state energies.

Contribution

It introduces a generalized NEO-based quantum algorithm with symmetry exploitation and improved initialization, enabling efficient near-term quantum simulations of molecular systems.

Findings

Achieved ground state energy accuracy within 10^{-6} Ha for H₂ and malonaldehyde.

Reduced qubit and gate counts through symmetry-based Hamiltonian tapering.

Demonstrated high fidelity results comparable to classical benchmark methods.

Abstract

Nuclear quantum phenomena beyond the Born-Oppenheimer approximation are known to play an important role in a growing number of chemical and biological processes. While there exists no unique consensus on a rigorous and efficient implementation of coupled electron-nuclear quantum dynamics, it is recognised that these problems scale exponentially with system size on classical processors and therefore may benefit from quantum computing implementations. Here, we introduce a methodology for the efficient quantum treatment of the electron-nuclear problem on near-term quantum computers, based upon the Nuclear-Electronic Orbital (NEO) approach. We generalize the electronic two-qubit tapering scheme to include nuclei by exploiting symmetries inherent in the NEO framework; thereby reducing the hamiltonian dimension, number of qubits, gates, and measurements needed for calculations. We also develop parameter transfer and initialisation techniques, which improve convergence behavior relative to conventional initialisation. These techniques are applied to H$_2$ and malonaldehyde for which results agree with Nuclear-Electronic Orbital Full Configuration Interaction and Nuclear-Electronic Orbital Complete Active Space Configuration Interaction benchmarks for ground state energy to within $10^{-6}$ Ha and entanglement entropy to within $10^{-4}$. These implementations therefore significantly reduce resource requirements for full quantum simulations of molecules on near-term quantum devices while maintaining high accuracy.