Pericyclic reactions provide stringent tests for quantum simulations because their mechanisms are governed by orbital symmetry and involve correlated transition states. In this work, we employ the variational quantum eigensolver (VQE) combined with a previously established symmetry-guided active-space selection protocol based on symmetry-matched fractions (SMF-VQE) to simulate Diel-Alder and Alder-ene reactions in complex systems involving extended pi-conjugation and multiple bonding. Although absolute electronic energies obtained from the current protocol exhibit significant deviations from the values computed using CCSD method, the symmetry-guided active spaces yield substantial cancellation of deviations in the energy differences. As a result, reaction energies are predicted with error (relative to CCSD) less than one kcal per mol, while activation energies are reproduced within about five to six kcal per mol. The symmetry-guided protocol also reduces the large combinatorial space of active-space choices to a single symmetry-consistent selection for each reaction.
Pericyclic reactions provide stringent tests for quantum simulations because their mechanisms are governed by orbital symmetry and involve correlated transition states. In this work, we employ the variational quantum eigensolver (VQE) combined with a previously established symmetry-guided active-space selection protocol based on symmetry-matched fractions (SMF-VQE) to simulate Diel-Alder and Alder-ene reactions in complex systems involving extended pi-conjugation and multiple bonding. Although absolute electronic energies obtained from the current protocol exhibit significant deviations from the values computed using CCSD method, the symmetry-guided active spaces yield substantial cancellation of deviations in the energy differences. As a result, reaction energies are predicted with error (relative to CCSD) less than one kcal per mol, while activation energies are reproduced within about five to six kcal per mol. The symmetry-guided protocol also reduces the large combinatorial space of active-space choices to a single symmetry-consistent selection for each reaction.
Simulation of chemical reactions on quantum computing platforms using quantum classical hybrid algorithms such as the Variational Quantum Eigensolver (VQE) is challenged by the need for a reaction consistent treatment of electron correlation in reaction energy evaluations. In this work, we employ a previously reported symmetry guided active space selection protocol to compute ring strain energies of cyclic hydrocarbons using homodesmotic reaction schemes. The protocol enforces symmetry consistency across all reactants and products by selecting active spaces that yield identical symmetry matched fraction (SMF) values, thereby ensuring balanced correlation treatment at the reaction level. When multiple active spaces satisfy this criterion for a given molecule, larger active spaces often provide improved correlation treatment; however, smaller symmetry consistent active spaces can also yield comparable agreement due to favorable error cancellation within the homodesmotic framework. Using this framework, ring strain energies were evaluated for a series of saturated and unsaturated cyclic hydrocarbons, ranging from cyclopropane to the structurally complex adamantane. The resulting energies achieve chemical accuracy relative to density functional theory (DFT) and remain in close agreement with coupled cluster singles and doubles (CCSD) benchmarks. The systematic performance across increasing molecular complexity highlights the effectiveness of combining homodesmotic reaction design with symmetry-consistent VQE calculations. This approach, which enforces physically grounded consistency across reaction species, demonstrates clear potential for extending reaction based quantum simulations to larger molecular systems and broader classes of chemical reactions.
Simulation of chemical reactions to compute reaction energies using variational algorithms remains challenging in achieving chemical accuracy relative to benchmark computational chemistry methods due to limitations such as qubit number, circuit depth, and noise. To address this issue, we propose the definition of different active spaces for studying chemical reactions, incorporating irreducible representations of both ground and excited states by defining the maximum contribution of excitation terms in the ansatz, implemented here within a second-order Trotterized UCCSD-VQE framework. Our results demonstrate that this approach can achieve chemical accuracy for several representative reactions and yields close agreement with benchmark methods across a broader range of reactions. For all reactions studied, the difference in reaction energies between VQE and CCSD remains within 1 kcal/mol. At the same time, comparison with FCI shows chemical accuracy for several cases and close agreement for the remaining systems. Furthermore, our analysis simplifies the selection of active spaces and electrons for each reaction, reducing it to a single optimal combination that supports chemically accurate or near-chemical-accuracy predictions.
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.
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 computing offers a compelling route to ab initio simulations of chemical reactions, while noisy intermediate-scale quantum (NISQ) hardware demands resource-aware protocols. In this study, we introduce an efficient workflow using a noise-resilient hardware-adaptable ansatz (HAA) in an active space combined with driven similarity renormalization group (DSRG) downfolding. The active space is obtained via a new selection algorithm, many-body-expanded correlation-energy active space (MBECAS), based on orbital ranking by first-/second-order correlation-energy increments. We validate the MBECAS-DSRG-HAA workflow on reactions with up to tens of atoms, reproducing Diels-Alder barriers within a few millihartrees after error mitigation. By combining an efficient active space selector, effective-Hamiltonian downfolding, and a low-depth variational circuit, our approach delivers highly accurate reaction energetics with modest quantum resources and motivates extensions to larger systems and excited-state dynamics.
The variational quantum eigensolver (VQE) has emerged as one of the leading quantum algorithms for solving electronic structure problems on near-term noisy intermediate-scale quantum devices. However, its practical application to quantum chemistry remains challenging due to the limited coherence time, imperfect quantum gate fidelity, and the large number of measurements required, which together confine current electronic structure simulations to relatively small active spaces. In this work, we present an orbital-optimized VQE framework based on orbital compression, designed to improve the accuracy of electronic structure calculations while maintaining relatively small active spaces. Frozen natural orbitals (FNO) and split virtual orbitals (SVO) are first employed to construct compact active spaces for VQE simulations, leading to the FNO/SVO-VQE approach. Orbital optimization is then incorporated to further recover electron correlation effects, resulting in the FNO/SVO-OO-VQE methods. We apply the proposed method to simulate potential energy surfaces for molecular dissociation and the activation energy of formaldehyde decomposition. Numerical results demonstrate that both FNO-OO-VQE and SVO-OO-VQE improve the variational accuracy while substantially reducing measurement cost.