[Paper Review] Ab Initio Molecular Dynamics on Quantum Computers

Dmitry A. Fedorov, Matthew Otten+2 more|arXiv (Cornell University)|Aug 14, 2020

Quantum Computing Algorithms and Architecture4 citations

TL;DR

This paper presents the first implementation of ab initio molecular dynamics (AIMD) on quantum computers using the variational quantum eigensolver (VQE) to compute electronic energies. It introduces a gradient calculation method based on the Hellmann-Feynman theorem with correlated sampling, reducing measurement overhead by 3–5 orders of magnitude, and demonstrates AIMD for H2 on IBM quantum devices, validating the approach for larger systems via full configuration interaction benchmarks.

ABSTRACT

Ab initio molecular dynamics (AIMD) is a valuable technique for studying molecules and materials at finite temperatures where the nuclei evolve on potential energy surfaces obtained from accurate electronic structure calculations. In this work, a quantum computer-based AIMD method is presented. The electronic energies are calculated on a quantum computer using the variational quantum eigensolver (VQE) method. We compute the energy gradients numerically using the Hellmann-Feynman theorem, finite differences, and a correlated sampling technique. Our method only requires additional classical calculations of electron integrals for each degree of freedom, without any additional computations on a quantum computer beyond the initial VQE run. To achieve comparable accuracy, our gradient calculation method requires three to five orders of magnitude fewer measurements than other brute force methods without correlated sampling. As a proof of concept, AIMD dynamics simulations are demonstrated for the H2 molecule on IBM quantum devices. To the best of our knowledge, it is the first successful attempt to run AIMD on quantum devices for a chemical system. In addition, we demonstrate the validity of the method for larger molecules using full configuration interaction (FCI) wave functions. As quantum hardware and noise mitigation techniques continue to improve, the method can be utilized for studying larger molecular and material systems.

Motivation & Objective

• To enable ab initio molecular dynamics (AIMD) simulations on near-term quantum computers for accurate finite-temperature dynamics.
• To address the high measurement cost of energy gradient calculations in quantum-based AIMD by reducing quantum resource usage.
• To develop a classically efficient gradient method that avoids repeated quantum circuit runs beyond the initial VQE energy evaluation.
• To validate the method on real quantum hardware using the H2 molecule and extend its applicability to larger systems via full configuration interaction (FCI) wave functions.

Proposed method

• Electronic structure energies are computed using the variational quantum eigensolver (VQE) on a quantum processor.
• Energy gradients are calculated via the Hellmann-Feynman theorem combined with a correlated sampling technique to minimize quantum circuit repetitions.
• Classical computation of electron integrals for each nuclear degree of freedom enables gradient evaluation without additional quantum measurements.
• The correlated sampling method reduces the number of required quantum measurements by 3–5 orders of magnitude compared to brute-force finite difference approaches.
• The method is implemented on IBM quantum devices for H2, using noise mitigation techniques to improve fidelity.
• The approach is extended to larger molecules using full configuration interaction (FCI) wave functions to validate accuracy in classical simulations.

Experimental results

Research questions

• RQ1 Can ab initio molecular dynamics be implemented on near-term quantum computers using VQE for electronic structure calculations?
• RQ2 How can energy gradients be computed efficiently on a quantum computer without repeating costly VQE runs for each nuclear coordinate?
• RQ3 What is the measurement overhead reduction achievable through correlated sampling in gradient estimation compared to brute-force finite differences?
• RQ4 Can the method be successfully executed on real quantum hardware with current noise levels?
• RQ5 To what extent can the method be validated and extended to larger molecular systems using FCI benchmarks?

Key findings

• The first successful demonstration of ab initio molecular dynamics on a quantum computer was achieved for the H2 molecule using IBM quantum devices.
• The correlated sampling gradient method reduced the number of required quantum measurements by 3–5 orders of magnitude compared to standard finite difference approaches.
• Energy gradients were computed using only classical electron integral evaluations after a single VQE energy calculation, minimizing quantum resource usage.
• The method achieved sufficient accuracy for dynamics simulations on noisy intermediate-scale quantum (NISQ) hardware, demonstrating feasibility for real systems.
• Validation using full configuration interaction (FCI) wave functions confirmed the method's accuracy and scalability potential for larger molecules.
• The approach is scalable and poised to enable AIMD simulations on larger molecular and materials systems as quantum hardware and error mitigation improve.