Abstract Efficient computation of molecular energies is an exciting application of quantum computing for quantum chemistry, but current noisy intermediate-scale quantum (NISQ) devices can only execute shallow circuits, limiting existing variational quantum algorithms, which require deep entangling quantum circuit ansatzes to capture correlations, to small molecules. Here we demonstrate a variational NISQ-friendly algorithm that generates a set of Hartree–Fock ansatzes using multiple shallow circuits with depth linear in the number of qubits to estimate electronic correlation energies via perturbation theory up to the second order. We tested the algorithm on several small molecules, both with classical simulations including noise models and on cloud quantum processors, showing that it not only reproduces the equilibrium molecular energies but it also captures the perturbative electronic correlation effects at longer bond distances. The number of shallow circuits required for our algorithms scales O ( N 5 ) , with N being the system size, thus enabling the study of larger molecules compared to other approaches, where circuit depth or number of qubits required become prohibitive for NISQ devices.
Molecule size correlates with the number of electrons on electronic energies and strength of anharmonicity on vibrational properties, however, it is challenging to address using classical computing. In this study, variational quantum eigensolver (VQE) algorithm was implemented on a quantum simulator to quantify electronic and vibrational energies and reaction pathways of CO2 + NH3 = NH2COOH. The VQE-based Hartree-Fock-Embedding algorithm was adopted to benchmark electronic energies for a series of molecules (doi.org/10.1063/5.0188249) and quantify the reaction energy profile of the CO2 capture reaction (doi.org/10.1116/5.0137750). The generated reaction profile is in good agreement with the classical high-level Coupled-Cluster-Singles-and-Doubles (CCSD) results. The quantum computing algorithm also helps enhance the calculation of vibrational ground-state energies by considering the many-body coupling using the Vibrational Self-Consistent Field method, providing results for CO2 and NH3 molecules with accuracy comparable to the direct diagonalization method. Our approach indicates quantum computing can be applied to solve practical problems.
Accurately describing strongly correlated electronic systems remains a central challenge in quantum chemistry, as electron-electron interactions give rise to complex many-body wavefunctions that are difficult to capture with conventional approximations. Classical wavefunction-based approaches, such as the Semistochastic Heat-bath Configuration Interaction (SHCI) and the Density Matrix Renormalization Group (DMRG), currently define the state of the art, systematically converging toward the Full Configuration Interaction (FCI) limit, but at a rapidly increasing computational cost. Quantum computing algorithms promise to alleviate this scaling bottleneck by leveraging entanglement and superposition to represent correlated states more compactly. We introduced the Handover-Iterative Variational Quantum Eigensolver (HI-VQE) as a practical quantum computing algorithm with an iterative "handover" mechanism that dynamically exchanges information between quantum and classical computers, even using Noisy Intermediate-Scale Quantum (NISQ) computers. In this work, we extend the HI-VQE to benchmark two prototypical strongly correlated systems, the nitrogen molecule
N2 and iron-sulfur (Fe-S) cluster, which serve as stringent tests for both classical and quantum electronic-structure methods. By comparing HI-VQE results against Heat-bath Configuration Interaction (HCI) benchmarks, we assess its accuracy, scalability, and ability to capture multireference correlation effects. Achieving quantitative agreement on these canonical systems demonstrates a viable pathway toward quantum-enhanced simulations of complex bioinorganic molecules, catalytic mechanisms, and correlated materials.
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.