The search for new tasks related to quantum chemical calculations that can be performed on current quantum computers is important for the development of both quantum computing and quantum chemical calculations. Although chemical reaction calculations have a wide range of applications in quantum chemical calculations, there is no quantum algorithm for obtaining the activation energy ($E_a$), which determines the rate of chemical reactions for any given substance. In this study, we propose a quantum algorithm for obtaining $E_a$ for a given substance by optimizing the reaction path via molecular geometry generation using quantum circuits. The nudged elastic band method was used to optimize a reaction path, and the ground state calculation for each state on the reaction path involved either variational quantum eigensolver (VQE) or exact diagonalization (ED). The proposed algorithm was applied to H2 + H -> H + H2 reaction, and the reaction path was correctly optimized. Moreover, the activation energy was obtained with good accuracy regardless of whether VQE or ED is used for the ground state calculation. The results demonstrate the feasibility of performing the chemical reaction calculations using quantum algorithms.
The search for new tasks related to quantum chemical calculations that can be performed on current quantum computers is important for the development of both quantum computing and quantum chemical calculations. Although chemical reaction calculations have a wide range of applications in quantum chemical calculations, there is no quantum algorithm for obtaining the activation energy (Ea), which determines the rate of chemical reactions for any given substance. In this study, we propose a quantum algorithm for obtaining Ea for a given substance by optimizing the reaction path via molecular geometry generation using quantum circuits. The nudged elastic band method was used to optimize a reaction path, and the ground state calculation for each state on the reaction path involved either variational quantum eigensolver (VQE) or exact diagonalization (ED). The proposed algorithm was applied to H2 + H -> H + H2 reaction, and the reaction path was correctly optimized. Moreover, the activation energy was obtained with good accuracy regardless of whether VQE or ED is used for the ground state calculation. The results demonstrate the feasibility of performing the chemical reaction calculations using quantum algorithms.
The search for new computational tasks of quantum chemistry that can be performed on current quantum computers is important for the development of quantum computing and quantum chemistry. Although calculations of chemical reactions have a wide range of applications in quantum chemical calculations, a quantum algorithm for obtaining activation energy Ea, which determines the rate of chemical reactions, has not been performed. In this study, we propose a quantum algorithm for the chemical reaction path optimization to obtain Ea. In our algorithm, quantum circuits can be used not only for the energy evaluation by the variational quantum eigensolver (VQE) but also for chemical reaction path generation. The chemical reaction path is obtained by encoding the initial reaction path to the circuit, operating parameterized gates, and extracting the path information by measurement. The nudged elastic band method was used for optimizing a reaction path, and the ground-state calculation for each state on the path was performed by the VQE or the exact diagonalization (ED). The proposed algorithm was applied to H2+H→H2+H reaction, and we confirmed that Ea was obtained accurately in the case of both the VQE and the ED. We also obtained numerical results that the entanglement between the images accelerates the path optimization. From these results, we show the feasibility of performing fast and accurate chemical reaction calculations by using quantum algorithms.
Quantum and hybrid quantum-classical algorithms have the potential to improve the accuracy and scale of quantum chemistry and impact a broad range of applications such as drug discovery and catalysis. In particular, subspace methods such as sample-based quantum diagonalization (SQD) can already tackle classically challenging systems. However, practical algorithms that go beyond the computation of electronic ground and excited states are still scarce. Here, we introduce the variable-geometry sample-based quantum diagonalization (VGSQD) algorithm, which extends SQD to variable molecular geometries by reusing quantum samples from a reference geometry at displaced ones, thus significantly reducing quantum computational cost. Using circuits of up to 124 qubits on ibm-quebec, an IBM Heron r2 quantum processor, we determine the equilibrium geometry and energy of the weakly bound, strongly correlated beryllium dimer, as well as the water molecule. Finally, we extend VGSQD to chemical reactions and compute the minimum energy path and energy barrier of a hydrogen exchange reaction. The results are comparable with state-of-the-art classical methods such as CCSD(T) and DMRG. This work broadens the scope of quantum algorithms for chemistry, from energies to geometry optimization and reaction pathways, both essential for practical applications.
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.
Quantum computers offer the potential to simulate chemical systems beyond the capabilities of classical computers. However, current quantum computing approaches to ab initio molecular dynamics (AIMD) and vibrational analysis largely rely on the Variational Quantum Eigensolver (VQE), whose circuit depth, iterative optimization, and measurement overhead hinder the practical simulation of molecular systems. Here, we extend Sample-based Quantum Diagonalization (SQD), a quantum sampling-based electronic-structure method, to AIMD and vibrational analysis on noisy quantum hardware. The resulting framework enables nuclear forces and Hessians to be derived from quantum-computed electronic energies, facilitating molecular dynamics and characterization of potential energy surfaces. We demonstrate the approach using diverse molecular processes, including H2 bond vibration, the proton-exchange reaction (H+ + H2), the bimolecular nucleophilic substitution (SN2) reaction (Cl- + CH3Cl), and proton-transfer dynamics between two water molecules involving transient formation of the Zundel cation (H2O···H+···OH2). Across these systems, SQD-AIMD trajectories and vibrational frequencies obtained with noisy quantum hardware/noise-models show excellent agreement with classical reference calculations and substantially improved accuracy relative to previously reported VQE-based simulations. Importantly, the SQD-based approach eliminates costly variational optimization and significantly reduces measurement requirements relative to VQE, enabling AIMD simulations spanning approximately 500 timesteps (∼200 fs), substantially longer than previously reported AIMD simulations on quantum hardware. These results establish SQD-AIMD and SQD-vibrational analysis as practical and scalable frameworks for simulating chemical reaction dynamics and elucidating reaction mechanisms on near-term quantum hardware, extending quantum computing applications beyond static electronic structure calculations.
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.
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.