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arXiv:2010.13578 · AIP conference proceedings

Benchmarking the variational quantum eigensolver through simulation of the ground state energy of prebiotic molecules on high-performance computers

Phalgun Lolur, Martin Rahm, Mårten Skogh, Laura García-Álvarez, Goran P. Wendin

Published Jan 1, 2021• 19 citations
arXivHTMLPDF

Abstract

We use the Variational Quantum Eigensolver (VQE) as implemented in the Qiskit software package to compute the ground state energy of small molecules derived from water, H2O, and hydrogen cyanide, HCN. The work aims to benchmark algorithms for calculating the electronic structure and energy surfaces of molecules of relevance to prebiotic chemistry, beginning with water and hydrogen cyanide, and to run them on the available simulated and physical quantum hardware. The numerical calculations of the algorithms for small quantum processors allow us to design more efficient protocols to be run in real hardware, as well as to analyze their performance. Future implementations on accessible quantum processing prototypes will benchmark quantum computers and provide tests of quantum advantage with heuristic quantum algorithms.

DOI
10.1063/5.0054915

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We use the Variational Quantum Eigensolver (VQE) as implemented in the Qiskit software package to compute the ground state energy of small molecules derived from water, H2O, and hydrogen cyanide, HCN. The work aims to benchmark algorithms for calculating the electronic structure and energy surfaces of molecules of relevance to prebiotic chemistry, beginning with water and hydrogen cyanide, and to run them on the available simulated and physical quantum hardware. The numerical calculations of the algorithms for small quantum processors allow us to design more efficient protocols to be run in real hardware, as well as to analyze their performance. Future implementations on accessible quantum processing prototypes will benchmark quantum computers and provide tests of quantum advantage with heuristic quantum algorithms.
Solving interacting multi-particle systems is a central challenge in quantum chemistry and condensed matter physics. In this work, we investigate the computation of ground states and ground-state energies for the He-H+ and H2O molecules using quantum computing techniques. We employ the variational quantum eigensolver (VQE), implemented both on a quantum computer simulator and on an IBM quantum device. The resulting energies are benchmarked against exact ground-state energies obtained via classical methods. Simulations of the H2O molecule were performed on Nottingham's High Performance Computing (HPC) facilities.
Quantum computing has emerged as a promising technology for solving problems that are intractable for classical computers. In this study, we introduce quantum computing and implement the Variational Quantum Eigensolver (VQE) algorithm using Qiskit on the IBM Quantum platform to calculate the ground state energy of a hydrogen molecule. We provide a theoretical framework of quantum mechanics, qubits, quantum gates, and the VQE algorithm. Our implementation process is described, and we simulate the results. Additionally, experiments are conducted on the IBM Quantum platform, and the results are analyzed. Our fi ndings demonstrate that VQE can effi ciently calculate molecular properties with high accuracy. However, limitations and challenges in scaling the algorithm for larger molecules are also identifi ed. This work contributes to the growing body of research on quantum computing and highlights the potential applications of VQE for real-world problem-solving.
Abstract Solving the electronic structure for multi-electronic systems is a hard problem. Even for small atoms and molecules, approximations have to be made in order to solve numerically the Schrödinger equation. Although different methods have been developed to take into account electron correlations, their computational cost reduces their feasibility. Quantum simulation provides an alternative to traditional computational methods for enquiring the electronic structure of molecules. Specifically, the Variational Quantum Eigensolver (VQE) algorithm provides a hybrid quantum-classical algorithm for the implementation on current near term quantum devices. In this work, we explore the implementation of VQE on Qiskit for calculating the ground-state energy of diatomic Hydrogen molecule.
In this research paper, we explore the application of quantum computing technologies, specifically the Variational Quantum Eigensolver, to accurately determine the ground state energies of small molecules, especially for molecules with higher bond orders. Our study showcases the feasibility and accuracy of quantum algorithms in performing complex quantum mechanical calculations for molecules like hydrogen, neon, water, methane, nitrogen, oxygen, ethyne, and ethene. Our results demonstrate high precision and reliability in molecular simulations with errors from theoretical values of less than 2 percent for most of the molecules. We also address the challenges associated with scalability and error rates when dealing with larger and more complex molecules. By combining the power of quantum computing with molecular simulations, we aim to enhance our understanding of molecular behavior, leading to more precise predictions in material science and drug discovery.
Abstract We present a comprehensive quantum chemical study of nine molecules H₂, HeH⁺, LiH, BeH₂, H₂O, NH₃, CH₄, CO₂, and N₂ using the Variational Quantum Eigensolver (VQE) algorithm implemented in Qiskit 2.4.1. Molecular Hamiltonians are constructed in the STO-3G minimal basis set, transformed to qubit operators via the Jordan-Wigner mapping, and optimized using the n-local hardware-efficient ansatz with the SLSQP optimizer. Ground state energies are benchmarked against Full Configuration Interaction (FCI)/STO-3G reference values from authoritative literature sources. VQE achieves accuracies from 96.46% (HeH⁺) to 99.99% (H₂), average 98.68%. Potential energy surfaces are generated for all nine molecules and compared with high level ab initio literature PES references including the Kolos-Wolniewicz H₂ curve, the Polyansky water surface, and the Bytautas-Ruedenberg N₂ FCI surface. Equilibrium bond lengths agree with experiment to within 0.000–0.006 Å. Quantum ansatz circuits are analyzed in detail for all molecules. These results confirm the viability of near-term VQE algorithms for molecular quantum chemistry across diverse bond types and geometries.
Feynmans ideas to employ quantum systems for simulating other quantum systems gave rise to quantum simulation. While current quantum computers are still prone to decoherence and rely on error correction, the development of hybrid algorithms that employ both quantumand classical computation allow to perform quantum simulation. Among these algorithms, the Variational Quantum Eigensolver algorithm has permitted to explore the electronic structure of simple atoms and molecules by exploiting the Rayleigh Ritz variational principle. In this work we provide the implementation of the VQE algorithm for finding the ground state energy of the hydrogen molecule on Qiskit library for python.