We demonstrate a quantum-classical workflow for ab initio molecular dynamics (AIMD) in which quantum measurements from a chemistry-inspired LUCJ ansatz are post-processed using Sample-based Quantum Diagonalization (SQD) to recover determinant subspaces and deliver energies and analytical nuclear gradients for dynamics. As an exact benchmark, we use full configuration interaction (FCI) in the STO-3G basis, enabling a direct assessment of the accuracy of SQD. In gas-phase benchmarks, SQD reproduces FCI energies and gradients to within 1 kcal mol$^{-1}$ of the FCI reference and yields stable AIMD trajectories. In explicit-solvent QM/MM simulations, SQD retains this agreement, matching FCI energy fluctuations and RMS gradient profiles and reproducing solute-solvent structure as quantified by radial distribution functions. Overall, these benchmarks establish LUCJ+SQD as a practical route for integrating current quantum hardware into QM/MM molecular dynamics and provide an early demonstration of condensed-phase QM/MM dynamics driven by a quantum electronic-structure engine.
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45 pages, 7 figures. Supporting Information included as an ancillary file
We demonstrate a quantum-classical workflow for ab initio molecular dynamics (AIMD) in which quantum measurements from a chemistry-inspired LUCJ ansatz are post-processed using Sample-based Quantum Diagonalization (SQD) to recover determinant subspaces and deliver energies and analytical nuclear gradients for dynamics. As an exact benchmark, we use full configuration interaction (FCI) in the STO-3G basis, enabling a direct assessment of the accuracy of SQD. In gas-phase benchmarks, SQD reproduces FCI energies and gradients to within 1 kcal mol−1 of the FCI reference and yields stable AIMD trajectories. In explicit-solvent QM/MM simulations, SQD retains this agreement, matching FCI energy fluctuations and RMS gradient profiles and reproducing solute-solvent structure as quantified by radial distribution functions. Overall, these benchmarks establish LUCJ+SQD as a practical route for integrating current quantum hardware into QM/MM molecular dynamics and provide an early demonstration of condensed-phase QM/MM dynamics driven by a quantum electronic-structure engine.
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.
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.
Ab initio molecular dynamics (AIMD) is a valuable technique for studying molecules and materials at finite temperatures where the nuclei evolve on potential energy surfaces obtained from accurate electronic structure calculations. In this work, we present an approach to running AIMD simulations on noisy intermediate-scale quantum (NISQ)-era quantum computers. The electronic energies are calculated on a quantum computer using the variational quantum eigensolver (VQE) method. Algorithms for computation of analytical gradients entirely on a quantum computer require quantum fault-tolerant hardware, which is beyond NISQ-era. Therefore, we compute the energy gradients numerically using finite differences, the Hellmann–Feynman theorem, and a correlated sampling technique. This method only requires additional classical calculations of electron integrals for each degree of freedom without any additional computations on a quantum computer beyond the initial VQE run. As a proof of concept, AIMD simulations are demonstrated for the H2 molecule on IBM quantum devices. In addition, we demonstrate the validity of the method for larger molecules using full configuration interaction wave functions. As quantum hardware and noise mitigation techniques continue to improve, the method can be utilized for studying larger molecular systems.
Accurate and efficient prediction of electronic wavefunctions is central to ab initio molecular dynamics (AIMD) and electronic structure theory. However, conventional ab initio methods require self-consistent optimization of electronic states at every nuclear configuration, leading to prohibitive computational costs, especially for large or strongly correlated systems. Here, we introduce a quantum-centric machine learning (QCML) model-a hybrid quantum-classical framework that integrates parameterized quantum circuits (PQCs) with Transformer-based machine learning to directly predict molecular wavefunctions and quantum observables. By pretraining the Transformer on a diverse dataset of molecules and ansatz types and subsequently fine-tuning it for specific systems, QCML learns transferable mappings between molecular descriptors and PQC parameters, eliminating the need for iterative variational optimization. The pretrained model achieves chemical accuracy in potential energy surfaces, atomic forces, and dipole moments across multiple molecules and ansatzes, and enables efficient AIMD simulations with infrared spectra prediction. This work establishes a scalable and transferable quantum-centric machine learning paradigm, bridging variational quantum algorithms and modern deep learning for next-generation molecular simulation and quantum chemistry applications.
The sample-based quantum diagonalization (SQD) method shows great promise in quantum-centric simulations of ground state energies in molecular systems. Inclusion of solute-solvent interactions in simulations of electronic structure is critical for biochemical and medical applications. However, all of the previous applications of the SQD method were shown for gas-phase simulations of the electronic structure. The present work aims to bridge this gap by introducing the integral equation formalism polarizable continuum model (IEF-PCM) of solvent into the SQD calculations. We perform SQD/cc-pVDZ IEF-PCM simulations of methanol, methylamine, ethanol, and water in aqueous solution using quantum hardware and compare our results to CASCI/cc-pVDZ IEF-PCM simulations. Our simulations on ibm_cleveland, ibm_kyiv, and ibm_marrakesh quantum devices are performed with 27, 30, 41, and 52 qubits demonstrating the scalability of SQD IEF-PCM simulations.
Quantum-selected configuration interaction (QSCI) methods use a quantum computer to identify dominant electronic configurations in the molecular ground state, while a classical computer diagonalizes the Hamiltonian within the reduced subspace spanned by those configurations. Sample-based quantum diagonalization (SQD), a leading QSCI approach, uses iterative classical post-processing to correct noisy quantum measurement to ensure that the corresponding configurations remain physically sensible. In this work, we show that SQD performance can be strongly influenced by uncontrolled growth of the classical diagonalization subspace. When classical resources are not explicitly constrained, classical uniform random sampling can reproduce SQD benchmarks as noise increases the diversity of sampled configurations. We show any fair benchmarking protocol of SQD must explicitly control diagonalization size over unique samples. We then address the problem of efficiently discovering physically relevant, energy-lowering configurations by introducing a measurement protocol based on non-orthogonal configuration interaction (NOCI). By distributing measurements across orbital bases optimized with respect to the molecular Hamiltonian, we obtain improved sample efficiency relative to measurements performed solely in the Hartree--Fock basis. Importantly, these improvements persist even under fixed classical resource budgets, demonstrating that the resulting configurations are of higher quality rather than being more numerous. Under our proposed benchmarking procedure, we establish measurement-basis engineering as a promising route to improving quantum sampling methods for electronic structure.