We present a hybrid quantum-classical framework for molecular simulations that combines the variational quantum eigensolver (VQE) with projection-based embedding (PBE) and an implicit solvation treatment. Solvent effects are incorporated through the solvation model based on density (SMD), enabling the investigation of chemically relevant processes in condensed phase environments within a quantum computing workflow. The embedding strategy partitions the molecular system into active and environment subsystems, allowing correlated quantum simulations of the chemically important subsystem while retaining an efficient classical description of the surroundings. As a representative application, we compute the potential energy surface of a bimolecular nucleophilic substitution (SN2) reaction between the chloride ion and chloromethane in multiple solvents, demonstrating that quantum eigensolver methods can be extended beyond gas-phase models to include solvent effects relevant for reaction energetics.
We present a hybrid quantum-classical framework for molecular simulations that combines the variational quantum eigensolver (VQE) with projection-based embedding (PBE) and an implicit solvation treatment. Solvent effects are incorporated through the solvation model based on density (SMD), enabling the investigation of chemically relevant processes in condensed phase environments within a quantum computing workflow. The embedding strategy partitions the molecular system into active and environment subsystems, allowing correlated quantum simulations of the chemically important subsystem while retaining an efficient classical description of the surroundings. As a representative application, we compute the potential energy surface of a bimolecular nucleophilic substitution (SN2) reaction between the chloride ion and chloromethane in multiple solvents, demonstrating that quantum eigensolver methods can be extended beyond gas-phase models to include solvent effects relevant for reaction energetics.
We present a combination of three-dimensional reference interaction site model self-consistent field (3D-RISM-SCF) theory and the variational quantum eigensolver (VQE) to consider the solvent distribution effects within the framework of quantum-classical hybrid computing. The present method, 3D-RISM-VQE, does not include any statistical errors from the solvent configuration sampling owing to the analytical treatment of the statistical solvent distribution. We apply 3D-RISM-VQE to compute the spatial distribution functions of solvent water around a water molecule, the potential and Helmholtz energy curves of NaCl, and to analyze the Helmholtz energy component and related properties of H 2 O and NH 4 + . Moreover, we utilize 3D-RISM-VQE to analyze the extent to which solvent effects alter the efficiency of quantum calculations compared with calculations in the gas phase using the L 1 -norms of molecular electronic Hamiltonians. Our results demonstrate that the efficiency of quantum chemical calculations on a quantum computer in solution is virtually the same as that in the gas phase.
Quantum chemical calculations on quantum computers have been focused mostly on simulating molecules in the gas phase. Molecules in liquid solution are, however, most relevant for chemistry. Continuum solvation models represent a good compromise between computational affordability and accuracy in describing solvation effects within a quantum chemical description of solute molecules. In this work, we extend the variational quantum eigensolver to simulate solvated systems using the polarizable continuum model. To account for the state dependent solute-solvent interaction we generalize the variational quantum eigensolver algorithm to treat non-linear molecular Hamiltonians. We show that including solvation effects does not impact the algorithmic efficiency. Numerical results of noiseless simulations for molecular systems with up to 12 spin-orbitals (qubits) are presented. Furthermore, calculations performed on a simulated noisy quantum hardware (IBM Q, Mumbai) yield computed solvation free energies in fair agreement with the classical calculations.
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.
Quantum embedding methods offer a promising route to extend quantum chemical calculations to large multiscale systems by treating a chemically important subsystem at a high level of theory while describing its surrounding environment at an affordable level. The methods are also quite relevant for quantum computing approaches based on hardware with limited resources. Here, we present an iterative projection-based embedding framework combined with VQE, in which the environment density is allowed to respond self-consistently to the refined electronic structure of the embedded subsystem described by VQE. Unlike conventional one-shot approaches where the environment remains frozen after the initial orbital optimization, the proposed iterative scheme alternates between the VQE-level treatment of the subsystem and a mean-field-level refinement of the environment until mutual self-consistency is achieved. The convergence behavior of the scheme is first examined using several small test systems. Its practical applicability is then demonstrated with a composite system with a CH2NH molecule sandwiched by two benzene rings, with the C=N dihedral angle rotating from 0 to 90 deg. The iterative procedure consistently converges within ~10 iteration steps across all tested geometries, yielding energies below the conventional one-shot embedding results. The converged results well reproduce the fully correlated reference energy employing the same active space, and the resulting potential energy surface with respect to the dihedral rotation is also in good agreement with the reference one. These results demonstrate that our iterative embedding framework is numerically robust and physically sound, yielding a self-consistent and reliable treatment of inter-subsystem correlation. We expect that its formulation will be particularly compatible with the emerging paradigm of quantum-classical hybrid computing.
We developed a method to include solvent effects on electronic transition calculations using quantum computing, employing the subspace-search variational quantum eigensolver (SSVQE) algorithm and the average solvent electrostatic configuration (ASEC) model. The SSVQE algorithm is used to calculate the energy of ground and excited states of organic molecules, and the ASEC model is used to describe the electrostatic contribution of the solvent effect at room temperature. By comparing the results with complete active space configuration interaction calculations, we demonstrate that the solvent effect is properly accounted for in the calculation of each state energy value performed by the quantum algorithm. Furthermore, the gas-liquid shift of the electronic transitions is also correctly described, with values that present semiquantitative agreement with results obtained through more sophisticated treatment using classical computers and experimental values, demonstrating that the solvation model is robust even when paired with quantum algorithms. The ASEC-SSVQE method opens the possibility of using noisy intermediate-scale quantum devices to study the spectroscopy properties of solvated molecules, with the inclusion of thermodynamic effects.
Quantum simulation of chemistry in realistic environments is constrained by the orbital cost of explicit solvent, ions, and other surroundings. We present the quantum-classical effective fragment potential (Q-EFP) method, in which a chemically active region is treated with a quantum algorithm and the environment is represented by the effective fragment potential (EFP) in GAMESS. Coulomb and polarization potentials enter the active-region one-electron Hamiltonian, while EFP-EFP and short-range environment contributions are assembled classically. Statevector UCCSD/STO-3G benchmarks for LiH in a mixed water/methanol environment, H2O in a five-water environment, and BeH2 in an ammonium/nitrate environment differ from matched classical CCSD/EFP calculations by 0.03, 0.38, and 0.01 kcal/mol, respectively. The active calculations require 4 to 8 qubits, compared with estimated full-system counts of approximately 84 to 246 qubits, corresponding to register reductions of about 10-fold to 35-fold. These proof-of-concept results validate the embedded Hamiltonian and Q-GAMESS workflow while separating environmental size from quantum-register size. Q-EFP is complementary to real-space Q-EFMO fragmentation and virtual-orbital Q-FVO reduction, enabling a layered route to larger solvated systems.