The analysis of a chemical reaction along the ground-state potential energy surface in conjunction with an unknown spin state is challenging because electronic states must be separately computed several times using different spin multiplicities to find the lowest energy state. However, in principle, the ground state could be obtained with just a single calculation using a quantum computer without specifying the spin multiplicity in advance. In the present work, ground-state potential energy curves for PtCO were calculated as a proof-of-concept using a variational quantum eigensolver (VQE) algorithm. This system exhibits a singlet-triplet crossover as a consequence of the interaction between Pt and CO. VQE calculations using a statevector simulator were found to converge to a singlet state in the bonding region, while a triplet state was obtained at the dissociation limit. Calculations performed using an actual quantum device provided potential energies within ±2 kcal/mol of the simulated energies after error mitigation techniques were adopted. The spin multiplicities in the bonding and dissociation regions could be clearly distinguished even in the case of a small number of shots. The results of this study suggest that quantum computing can be a powerful tool for the analysis of the chemical reactions of systems for which the spin multiplicity of the ground state and variations in this parameter are not known in advance.
Classical simulation of molecular electronic structure is often limited by the rapid increase in computational cost associated with describing electron correlation. The Variational Quantum Eigensolver (VQE) is one hybrid quantum-classical approach ideally adapted to the Noisy Intermediate-Scale Quantum (NISQ) regime. This work applies the VQE algorithm to compute ground state energies of a set of molecules:
H2,H3+,LiH,HF,OH−,H2O,BH3,CH4, and
NH3. The approach utilizes the Unitary Coupled Cluster for Single and Double excitations (UCCSD) ansatz along with the Bravyi-Kitaev transformation for fermionic-to-qubit encoding. Quantum simulation outputs are systematically benchmarked against Full Configuration Interaction (FCI), a numerically exact traditional approach, and Unrestricted Hartree-Fock (UHF). The results establish a robust consistency of the VQE-obtained molecular ground state energies against standard FCI and UHF benchmarks. This research provides a critical benchmark, confirming that VQE has the capability for high-precision molecular simulations and playing the role of a pivotal stepping stone toward revolutionizing applications in drug discovery and materials science.
The electronic energies of molecules have been successfully evaluated on quantum computers. However, more attention is paid to the dynamics simulation of molecules in practical applications. Based on the variational quantum eigensolver (VQE) algorithm, Fedorov et al. proposed a correlated sampling (CS) method and demonstrated the vibrational dynamics of H2 molecules [J. Chem. Phys. 154, 164103 (2021)]. In this study, we have developed a quantum approach by extending the CS method based on the VQE algorithm (labeled eCS-VQE) for simulating chemical reaction dynamics. First, the CS method is extended to the three-dimensional cases for calculation of first-order energy gradients, and then, it is further generalized to calculate the second-order gradients of energies. By calculating atomic forces and vibrational frequencies for H2, LiH, H+ + H2, and Cl- + CH3Cl systems, we have seen that the approach has achieved the CCSD level of accuracy. Thus, we have simulated dynamics processes for two typical chemical reactions, hydrogen exchange and chlorine substitution, and obtained high-precision reaction dynamics trajectories consistent with the classical methods. Our eCS-VQE approach, as measurement expectations and ground-state wave functions can be reused, is less demanding in quantum computing resources and is, therefore, a feasible means for the dynamics simulation of chemical reactions on the current noisy intermediate-scale quantum-era quantum devices.
In the near future, material and drug design may be aided by quantum computer assisted simulations. These have the potential to target chemical systems intractable by the most powerful classical computers. However, the resources offered by contemporary quantum computers are still limited, restricting the simulations to very simple molecules. In order to rapidly scale up to more interesting molecular systems, we propose the embedding of the quantum electronic structure calculation into a classically computed environment obtained at the Hartree-Fock (HF) or density functional theory (DFT) level of theory. This result is achieved by constructing an effective Hamiltonian that incorporates a mean field potential describing the action of the inactive electrons on a selected Active Space (AS). The ground state of the AS Hamiltonian is then determined by means of the variational quantum eigensolver algorithm. We show that with the proposed HF and DFT embedding schemes, we can obtain significant energy corrections to the reference HF and DFT calculations for a number of simple molecules in their strongly correlated limit (the dissociation regime) as well as for systems of the size of the oxirane molecule.
Quantum chemical calculations have attracted much attention as a practical application of quantum computing. Quantum computers can prepare superpositions of electronic states with various numbers of electrons on qubits. This special feature could be used to construct an efficient method for analyzing the structural variations of molecules and chemical reactions involving changes in molecular charge. The present work demonstrates a variational quantum eigensolver (VQE) algorithm based on a cost function (
Lcost) having the same form as the grand potential of the grand canonical ensemble of electrons. The chemical potential of the electrons (
w) is used as an input to these VQE calculations, whereas the molecular charge is not specified in advance but rather is a physical quantity that results from the calculations. Calculations involving model systems are carried out to show the viability of this new approach. Calculations for typical electron-donating and electron-accepting molecules using this technique yielded cationic, neutral or anionic species depending on the value of
w. Models representing the adsorption of water or ammonia on copper-based catalysts predicted that oxidation would be associated with such adsorption. The molecular structures in which such reactions occurred were found to be dependent on the catalyst model, the adsorbed molecular species, and the value of
w. These results arise because the electronic state that gives the lowest
Lcost value depends on the value of
w and the molecular structure. This behaviour was successfully simulated by the present VQE calculations.
Abstract Context The variational quantum eigensolver (VQE) is a quantum-classical algorithm for estimating molecular ground-state energies. However, the accuracy depends on the choice of ansatz , active space, and initial variational parameters. Hence, it is relevant to perform assessments of VQE. The dissociation profiles of H
2 2 , H
3+ 3 + , and CH
5+ 5 + were chosen for these assessments. For H
2 2 and H
3+ 3 + , the UCCSD, GateFabric, and k -UpCCGSD ansätze reproduced the dissociation profiles with high accuracy. For CH
5+ 5 + , GateFabric and k -UpCCGSD provided the best compromise between accuracy and scalability. Hardware-efficient ansätze (HEA), particularly HEA-A and HEA-B, produced significant deviations from the reference energies. The results also demonstrate that larger numbers of parameters or logic gates do not necessarily improve VQE performance. Furthermore, some ansätze , especially GRSD and EHA, showed sensitivity to the initialization of the parameters. Methods Reference geometries and energies were obtained at the CISD/STO-3 G level using Gaussian 09. VQE simulations were performed with the PennyLane library employing the Jordan-Wigner mapping. The ansätze evaluated were UCCSD, k -UpCCGSD, GateFabric, GRSD, HEA-A, HEA-B, HEA-C, and Entanglement-variational Hardware-efficient Ansatz (EHA). Dissociation profiles were generated by varying interatomic distances and angular coordinates for H
2 2 and H
3+ 3 + , as well as the C-H
2 2 dissociation coordinate for CH
5+ 5 + . Active-space ranging from 2/2 to 8/8 electrons/orbitals was employed for CH
5+ 5 + . Variational parameters were optimized using stochastic gradient descent with a convergence threshold of
1×10−6 1 × 10