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.
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.
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.
Knowing the ground state energies of molecules and atoms gives scientists critical insight into these particles' behavior in reactions, thermodynamic and molecular properties, and excitation energies.However, due to the quantum mechanical nature of particles, finding the ground state of a system is intractable, both mathematically and experimentally.Computational methods are utilized to estimate the ground state energies.As we approach the limits of classical computers, quantum computers are viewed as promising alternatives that present a bright future for computational chemistry.In this paper, I review classical and quantum algorithms/methods for computational chemistry.Then, I discuss the current topics in using quantum computers for computational chemistry by analyzing the performance of the Variational Quantum Eigensolver (VQE) in different contexts on IBM's noisy quantum computer simulator, "QasmSimulator," and one of IBM's quantum computers, ibmq_belem.This review presents a theoretical and practical view of quantum computational chemistry.It allows the reader to learn the theory behind the algorithms and implement them with the guidance of the presented code and its detailed explanations.The purpose of this paper is to leave the reader with the necessary theory and adequate programming reference to implement the algorithms in various contexts.
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.
To understand the properties and interactions of materials, and determining the ground state energies is one of the important challenges in quantum chemistry, materials science, and quantum mechanics, where quantum computing can play an important role for studying the properties of materials. In this study, we have explored the quantum processor application to compute the He molecule ground state energy which utilizes the Variational Quantum Eigensolver (VQE) algorithm. In here, we have implemented VQE on a state-of-the-art quantum processor, optimizing a parameterized quantum circuit to minimize the energy expectation value of the He molecule's Hamiltonian on the four qubits processor. The obtained results of this work show a significant improvement in accuracy compared to classical computational methods, such as Hartree-Fock and density functional theory, which demonstrate the compute potential of quantum algorithms in quantum many-body problems. Thus, these results demonstrate the advantages of quantum computing in achieving high accuracy in simulations of molecular and material properties, and pave the way for future applications in more complex systems. This work highlights the potential of quantum processors in the fields of quantum chemistry, computational physics, and data science.
Exponential scaling presents a significant challenge in electronic structure calculations performed on classical computers. This paper explores how quantum computer algorithms can accurately represent quantum systems. Variational Quantum Eigensolver (VQE) algorithm is used to compute the ground state energy of hydrogen and helium sequences by implementing variational principle and quantum gates as trial wavefunction. This technique combines classical optimization with quantum computing calculations to simulate quantum systems on noisy and resource-limited computers. The resulting calculated energy is highly consistent to the corresponding exact values and Hartree-Fock calculations with a trend of when the number of atoms increases the calculated energy becomes more negative, leading to a decrease in the percentage error. Moreover, the convergence of the ground state energy of hydrogen and helium atoms was effectively optimized. The desired energy was reached, proven by adjusting the expectation value, and gradually achieving unity in state overlap. These findings demonstrate the VQE method's accuracy in calculating simple quantum systems and its scalability for larger atomic and molecular system, such as those in quantum chemistry and material science. However, challenges in quantum computer simulations, such as limited in qubit numbers and the presence of noise, require further advancements. Therefore, implementing a larger basis sets, advanced qubit mapping, specific chemistry ansatz, and flexible optimization techniques is one way to improve overall calculation.
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.