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.
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.
CO2 capture is critical to solving global warming. Amine-based solvents are extensively used to chemically absorb CO2. Thus, it is crucial to study the chemical absorption of CO2 by amine-based solvents to better understand and optimize CO2 capture processes. Here, we use quantum computing algorithms to quantify molecular vibrational energies and reaction pathways between CO2 and a simplified amine-based solvent model—NH3. Molecular vibrational properties are important to understanding kinetics of reactions. However, the molecule size correlates with the strength of anharmonicity effect on vibrational properties, which can be challenging to address using classical computing. Quantum computing can help enhance molecular vibrational calculations by including anharmonicity. We implement a variational quantum eigensolver (VQE) algorithm in a quantum simulator to calculate ground state vibrational energies of reactants and products of the CO2 and NH3 reaction. The VQE calculations yield ground vibrational energies of CO2 and NH3 with similar accuracy to classical computing. In the presence of hardware noise, Compact Heuristic for Chemistry (CHC) ansatz with shallower circuit depth performs better than Unitary Vibrational Coupled Cluster. The “Zero Noise Extrapolation” error-mitigation approach in combination with CHC ansatz improves the vibrational calculation accuracy. Excited vibrational states are accessed with quantum equation of motion method for CO2 and NH3. Using quantum Hartree–Fock (HF) embedding algorithm to calculate electronic energies, the corresponding reaction profile compares favorably with Coupled Cluster Singles and Doubles while being more accurate than HF. Our research showcases quantum computing applications in the study of CO2 capture reactions.
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.
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, andNH3. 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.
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.
Abstract Quantum computing is a technology that utilizes the principles of quantum mechanics to perform complex computational processes. In this work, we use Qiskit Module from IBM to do quantum computational calculation using Variational Quantum Eigensolver (VQE) algorithm. VQE is a hybrid quantum-classical method that combines a quantum computer to measure energies and a classical computer to process the measurement results and update the parameters of the quantum computer. The purpose of VQE is to find the ground state energy of a chemical system. In the previous study, many of the VQE calculations have been done on simple molecules. So, in this study, we would like to use Hydrazine molecule as our object of VQE calculation. Furthermore, these results will be compared with the results from the classical calculation (MP2, CCSD(T), QCISD(T), and CASSCF) methods for testing the effectiveness of VQE using Unitary Coupled-Cluster Single and Double excitations (UCCSD) Ansatz. The quantum algorithm based on the UCCSD Ansatz led to a simplification of the algorithm by reducing the circuit depth. Then, the possibility to use active space approximation, can be used to reduce the quantum gates while trying to keep a good level of accuracy. In this study, we chose (2,2) and (4,4) active spaces. Based on the results, as we increase the size of the active space during the evaluation of the single-point energy, the estimated ground states obtained from the VQE algorithm yield nearly identical values. Conversely, in CASSCF calculations, expanding the active space introduces more energy corrections, thus making it more sensitive. Additionally, when examining potential energy surfaces, VQE demonstrates results that gradually align with CCSD(T) and QCISD(T) methods.
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.