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.
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.
We present the quantum effective fragment molecular orbital (Q-EFMO) method, a hybrid framework that evaluates selected molecular-fragment correlation energies with the variational quantum eigensolver and assembles them through the size-consistent EFMO energy expression. A Hartree-Fock EFMO calculation supplies monomer references, many-body polarization, and distant-pair EFP interactions; independent VQE/UCCSD calculations provide correlation increments for monomers and selected near-field dimers. Consequently, the maximum quantum register is determined by the largest active fragment or fragment pair rather than by total system size. For a three-layer LiH benchmark in STO-3G, a full 2.5 to 3.5 Angstrom separation scan shows that two orbital-reduction schemes approach the full CCSD reference monotonically. The more aggressive scheme remains below 1 kcal/mol for separations of 2.6 Angstrom and greater and reaches 0.10 kcal/mol at 3.5 Angstrom, using 6 qubits for monomers and 12 for the largest dimers, compared with 14 qubits for the frozen-core dimer baseline. An implementation-specific cost proxy decreases from 1000 to 40, a factor of 25. These noise-free results establish the equations, software path, and resource scaling; broader chemical validation, larger bases, and hardware tests remain necessary.
Present-day sample-based quantum algorithms within quantum-centric supercomputing workflows require substantial classical post-processing, large circuit depths to produce chemically relevant samples, and long QPU times to execute the many circuits needed for molecules of chemically relevant size. We introduce FMO-QVM-HCI-HSQD, a resource-efficient sample-based framework that breaks a large problem into fragments, runs the fragments in parallel on virtual regions of the QPU, and reduces circuit depth through a half-qubit ansatz whose samples seed an HCI expansion. We demonstrate the algorithm on ibm_marrakesh and ibm_boston for the water trimer and the carmofur_Mpro complex with up to 52 qubits, benchmarking against FMO-CCSD(T), FMO-CASCI and FMO-HCI. For the water trimer (14 spin orbitals for monomers, 28 for dimers), our method reduces the two-qubit depth by 39% compared to FMO-QVM-SQD and the QPU time by 82% compared to sequential FMO-SQD, and accesses 3% of the determinant subspace versus 40% for FMO-SQD, while achieving more accurate energies. For the carmofur_Mpro complex (16 and 32 spin orbitals), it reduces the two-qubit depth by 47% and the QPU time by 20% compared to FMO-QVM-SQD, and accesses 0.007% of the determinant subspace versus 40%, while remaining within chemical accuracy. Extending the carmofur_Mpro active space in the 6-31G basis to 52 and 104 spin orbitals, sampled on 26 and 52 qubits, the total energy deviates from FMO-HCI by only 1.22 mHa. These results show that combining fragmentation, virtual QPU partitioning and half-qubit sampling makes sample-based quantum simulation of chemically relevant systems feasible on current hardware.
We present a large-scale experimental study of quantum-computing-based molecular simulation carried out on IQM's Sirius 24-qubit superconducting processor, utilizing up to 16 operational qubits. The work employs Sample-based Quantum Diagonalization (SQD) together with the Local Unitary Cluster Jastrow (LUCJ) ansatz to estimate ground-state energies for a set of benchmark molecules, including H2, LiH, BeH2, H2O, and NH3. In addition, we introduce a Linear-CNOT variant of the Unitary Coupled-Cluster Singles and Doubles (LCNot-UCCSD) ansatz within the SQD workflow, trading higher circuit depth for reduced classical preprocessing. A comparison between these ansätze is provided, clarifying their respective strengths, limitations, and suitability for near-term quantum hardware. We further explore potential energy landscapes through 1D scans for H2 and HeH+ using both STO-3G and 6-31G basis sets, and for LiH and BeH2 in STO-3G. Extending beyond this, we demonstrate the experimental construction of a full 2D potential energy surface for the water molecule on quantum hardware, mapped over a 32 × 32 grid in bond length and bond angle. To move beyond small benchmark systems, we combine SQD(LUCJ) with Density Matrix Embedding Theory (DMET) to compute active-space energies for a set of ligand-like molecules, as well as the pharmacologically relevant amantadine system. Across all studies, the majority of quantum-computed energies agree with reference FCI results, as well as with DMET-CASCI energies for embedded systems, to within chemical accuracy for the chosen basis sets. These results demonstrate the reliability of sample-based diagonalization approaches and underscore the potential of hybrid embedding strategies for extending quantum simulations to increasingly complex molecular systems, while also highlighting their practicality on current IQM quantum hardware.
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 multilevel embedding framework for quantum chemistry calculations on a quantum computer. In our framework, a quantum algorithm treats the strongly correlated active space, while a high-level wave-function method such as coupled cluster theory or multireference perturbation theory recovers the remaining correlation in the surrounding region. A sampling-based quantum algorithm, quantum-selected configuration interaction, bridges the quantum and classical treatments. The entire calculation is embedded in a low-cost density functional theory description of the surrounding environment using Manby's projection technique. We apply the framework to organic, metal-organic, and metallic systems, computing bond dissociation energies, adsorption energies, and reaction barriers using only the subset of qubits of a 144-qubit superconducting quantum computer at the University of Osaka and achieving $\sim$1 kcal/mol agreement with classical references for a Menshutkin SN2 reaction inside a carbon nanotube. Our results may open the way to quantitatively reliable quantum-classical hybrid calculations for large-scale chemical systems.
Quantum computers offer significant potential for complex system analysis, yet their application in large systems is hindered by limitations such as qubit availability and quantum hardware noise. While the variational quantum eigensolver (VQE) was proposed to address these issues, its scalability remains limited. Many efforts, including new ansätze and Hamiltonian modifications, have been made to overcome these challenges. In this work, we introduced the novel Fragment Molecular Orbital/Variational Quantum Eigensolver (FMO/VQE) algorithm. This method combines the fragment molecular orbital (FMO) approach with VQE and efficiently utilizes qubits for quantum chemistry simulations. Employing the UCCSD ansatz, the FMO/VQE achieved an absolute error of just 0.053 mHa with 8 qubits in a [Formula: see text] system using the STO-3G basis set, and an error of 1.376 mHa with 16 qubits in a [Formula: see text] system with the 6-31G basis set. These results indicated a significant advancement in scalability over conventional VQE, maintaining accuracy with fewer qubits. Therefore, our FMO/VQE method exemplifies how integrating fragment-based quantum chemistry with quantum algorithms can enhance scalability, facilitating more complex molecular simulations and aligning with quantum computing advancements.