Quantum chemistry simulations of some industrially relevant molecules are reported, employing variational quantum algorithms for near-term quantum devices. The energies and dipole moments are calculated along the dissociation curves for lithium hydride (LiH), hydrogen sulfide, lithium hydrogen sulfide, and lithium sulfide. In all cases, we focus on the breaking of a single bond to obtain information about the stability of the molecular species being investigated. We calculate energies and a variety of electrostatic properties of these molecules using classical simulators of quantum devices, with up to 21 qubits for lithium sulfide. Moreover, we calculate the ground-state energy and dipole moment along the dissociation pathway of LiH using IBM quantum devices. This is the first example, to the best of our knowledge, of dipole moment calculations being performed on quantum hardware.
Quantum chemistry simulations of some industrially relevant molecules are reported, employing variational quantum algorithms for near-term quantum devices. The energies and dipole moments are calculated along the dissociation curves for lithium hydride (LiH), hydrogen sulfide, lithium hydrogen sulfide, and lithium sulfide. In all cases, we focus on the breaking of a single bond to obtain information about the stability of the molecular species being investigated. We calculate energies and a variety of electrostatic properties of these molecules using classical simulators of quantum devices, with up to 21 qubits for lithium sulfide. Moreover, we calculate the ground-state energy and dipole moment along the dissociation pathway of LiH using IBM quantum devices. This is the first example, to the best of our knowledge, of dipole moment calculations being performed on quantum hardware.
This software supports the paper, "Exploring the scaling limitations of the variational quantum eigensolver with the bond dissociation of hydride diatomic molecules," published in the International Journal of Quantum Chemistry, whose abstract is as follows: Materials simulations involving strongly correlated electrons pose fundamental challenges to state-of-the-art electronic structure methods but are hypothesized to be the ideal use case for quantum computing. To date, no quantum computer has simulated a molecule of a size and complexity relevant to real-world applications, despite the fact that the variational quantum eigensolver (VQE) algorithm can predict chemically accurate total energies. Nevertheless, because of the many applications of moderately-sized, strongly correlated systems, such as molecular catalysts, the successful use of the VQE stands as an important waypoint in the advancement toward useful chemical modeling on near-term quantum processors. In this paper, we take a significant step in this direction. We lay out the steps, write, and run parallel code for an (emulated) quantum computer to compute the bond dissociation curves of the TiH, LiH, NaH, and KH diatomic hydride molecules using VQE. TiH was chosen as a relatively simple chemical system that incorporates d orbitals and strong electron correlation. Because current VQE implementations on existing quantum hardware are limited by qubit error rates, the number of qubits available, and the allowable gate depth, recent studies have focused on chemical systems involving s and p block elements. Through VQE + UCCSD calculations of TiH, we evaluate the near-term feasibility of modeling a molecule with d-orbitals on real quantum hardware. We demonstrate that the inclusion of d-orbitals and the use of the UCCSD ansatz, which are both necessary to capture the correct TiH physics, dramatically increase the cost of this problem. We estimate the approximate error rates necessary to model TiH on current quantum computing hardware using VQE+UCCSD and show them to likely be prohibitive until significant improvements in hardware and error correction algorithms are available.
Quantum simulations of the hydroxide anion and hydroxyl radical are reported, employing variational quantum algorithms for near-term quantum devices. The energy of each species is calculated along the dissociation curve, to obtain information about the stability of the molecular species being investigated. It is shown that simulations restricted to valence spaces incorrectly predict the hydroxyl radical to be more stable than the hydroxide anion. Inclusion of dynamical electron correlation from nonvalence orbitals is demonstrated, through the integration of the variational quantum eigensolver and quantum subspace expansion methods in the workflow of N -electron valence perturbation theory, and shown to correctly predict the hydroxide anion to be more stable than the hydroxyl radical, provided that basis sets with diffuse orbitals are also employed. Finally, we calculate the electron affinity of the hydroxyl radical using an aug-cc-pVQZ basis on IBM’s quantum devices.
With rapid progress being made in the development of platforms for quantum computation, there has been considerable interest in whether present-day and near-term devices can be used to solve problems of relevance. A commonly cited application area is the domain of quantum chemistry. While most experimental demonstrations of quantum chemical calculations on quantum devices have focused on the ground-state electronic energy of the system, other properties of the ground state, such as the electric dipole moment, are also of interest. Here, we employ the quantum-computed-moments method, based on the Lanczos cluster expansion, to estimate the dipole moment of the water molecule on an IBM Quantum superconducting quantum device. The noise-mitigated results agree with full-configuration-interaction calculations to within 0.03 ± 0.007 D ( 2 % ± 0.5 % ), compared with direct expectation-value determination (i.e., variational quantum eigensolver, VQE) with errors of the order of 0.07 D (5%), even when the VQE calculation is performed without noise. This demonstrates that moments-based energy-estimation techniques can be adapted to noise-robust evaluation of nonenergetic ground-state properties of chemical systems. We emphasize that the dipole moment is chosen as an example of such a property, but the method applies to any property determined by one- or two-body interactions.
Hybrid quantum-classical algorithms offer a promising pathway to address computational challenges in domains such as chemistry, physics, and materials science. In this work, we present a hybrid embedding framework to simulate the dative interaction between a lithium ion and a pyridine molecule. This represents the first implementation of quantum hardware for evaluating the binding energy of a non-covalent dative-bonded complex. Due to the current limitations of classical simulators and noisy intermediate-scale quantum (NISQ) devices—typically restricted to circuits with a few dozen qubits—we employ an embedding strategy where a chemically active region is treated on a quantum processor, and the remainder is modeled classically. Without error mitigation, results from quantum hardware show notable deviations from exact energies. To address this, we implement two combined error mitigation strategies, CEM1 and CEM2, both of which significantly improve total energy estimates. This work highlights the practical potential of variational quantum algorithms for studying complex molecular systems relevant to catalysis, hydrogen storage, and battery technologies.
Abstract Materials simulations involving strongly correlated electrons pose fundamental challenges to state‐of‐the‐art electronic structure methods but are hypothesized to be the ideal use case for quantum computing algorithms. To date, no quantum computer has simulated a molecule of a size and complexity relevant to real‐world applications, despite the fact that the variational quantum eigensolver (VQE) algorithm can predict chemically accurate total energies. Nevertheless, because of the many applications of moderately sized, strongly correlated systems, such as molecular catalysts, the successful use of the VQE stands as an important waypoint in the advancement toward useful chemical modeling on near‐term quantum processors. In this paper, we take a significant step in this direction. We lay out the steps, write, and run parallel code for an (emulated) quantum computer to compute the bond dissociation curves of the TiH, LiH, NaH, and KH diatomic hydride molecules using the VQE. TiH was chosen as a relatively simple chemical system that incorporates d orbitals and strong electron correlation. Because current VQE implementations on existing quantum hardware are limited by qubit error rates, the number of qubits available, and the allowable gate depth, recent studies using it have focused on chemical systems involving s and p block elements. Through VQE + UCCSD calculations of TiH, we evaluate the near‐term feasibility of modeling a molecule with d‐orbitals on real quantum hardware. We demonstrate that the inclusion of d‐orbitals and the use of the UCCSD ansatz, which are both necessary to capture the correct TiH physics, dramatically increase the cost of this problem. We estimate the approximate error rates necessary to model TiH on current quantum computing hardware using VQE + UCCSD and show them to likely be prohibitive until significant improvements in hardware and error correction algorithms are available.
This study investigates the Variational Quantum Eigensolver (VQE), a hybrid quantum-classical algorithm that partitions the computational workload between a quantum processing unit and a classical optimiser to determine the ground-state energies of molecular systems. The Qiskit SDK v1.x framework is employed, utilising the PySCFDriver module within the qiskit-nature package to construct second-quantised molecular electronic Hamiltonians for two representative systems: Hydrogen ( ) and Lithium Hydride ( ). For the complete active space is retained without spatial reduction, mapping the full Hamiltonian onto a 4-qubit register. However for the full STO-3G representation demands 12 qubits, rendering direct classical parameter optimisation computationally intractable. This bottleneck is resolved by applying an ActiveSpaceTransformer (num_electrons=2, num_spatial_orbitals=3) to freeze the chemically inactive lithium core electrons, reducing the active register to 6 qubits. Fermionic operators are subsequently converted to Pauli strings via the Jordan-Wigner transformation ( ) enabling the quantum processor to evaluate the molecular Hamiltonian as a circuit while preserving the fermionic anti-commutation relations. Under ideal, noise-free simulation using the StatevectorEstimator primitive paired with the COBYLA optimiser (maxiter=200), all VQE energy points converge precisely onto the Full Configuration Interaction (FCI) classical baseline across the full range of interatomic separations. This confirms that the hardware-efficient TwoLocal ansatz ( rotation layers and entanglement layers with reps=3) possesses sufficient expressive power to capture the molecular ground-state wavefunction. Introducing gate-level noise through AerSimulator backends calibrated from the FakeManilaV2 and FakeNairobiV2 hardware profiles—with optimisation driven by the SPSA algorithm (maxiter=150)—reveals two critical failure modes. A systematic upward energy bias is observed, attributable to depolarising gate errors and measurement readout faults that prevent the optimiser from reaching the true minimum energy eigenvalue. Additionally, severe stochastic oscillations between 1.0 Å and 1.5 Å on the curve induce premature convergence of the SPSA optimiser to spurious local minima. These results demonstrate that unmitigated hardware noise renders VQE incapable of reliably predicting equilibrium bond lengths on current NISQ devices, motivating the future integration of Zero-Noise Extrapolation (ZNE), readout error mitigation, and Virtual Distillation into the computational pipeline. Keywords—Variational Quantum Eigensolver (VQE); Qiskit 1.x; Potential Energy Curve; Molecular Ground-State Energy; Hardware-Efficient Ansatz; Gate-Level Noise Simulation; ActiveSpaceTransformer; NISQ Devices.