Hybrid quantum-classical algorithms offer a promising pathway to address computational challenges in domains such as chemistry, physics, and materials science. In this work, we present a hybrid embedding framework to simulate the dative interaction between a lithium ion and a pyridine molecule. This represents the first implementation of quantum hardware for evaluating the binding energy of a non-covalent dative-bonded complex. Due to the current limitations of classical simulators and noisy intermediate-scale quantum (NISQ) devices—typically restricted to circuits with a few dozen qubits—we employ an embedding strategy where a chemically active region is treated on a quantum processor, and the remainder is modeled classically. Without error mitigation, results from quantum hardware show notable deviations from exact energies. To address this, we implement two combined error mitigation strategies, CEM1 and CEM2, both of which significantly improve total energy estimates. This work highlights the practical potential of variational quantum algorithms for studying complex molecular systems relevant to catalysis, hydrogen storage, and battery technologies.
Hybrid quantum-classical algorithms offer a promising pathway to address computational challenges in domains such as chemistry, physics, and materials science. In this work, we present a hybrid embedding framework to simulate the dative interaction between a lithium ion and a pyridine molecule. This represents the first implementation of quantum hardware for evaluating the binding energy of a non-covalent dative-bonded complex. Due to the current limitations of classical simulators and noisy intermediate-scale quantum (NISQ) devices—typically restricted to circuits with a few dozen qubits—we employ an embedding strategy where a chemically active region is treated on a quantum processor, and the remainder is modeled classically. Without error mitigation, results from quantum hardware show notable deviations from exact energies. To address this, we implement two combined error mitigation strategies, CEM1 and CEM2, both of which significantly improve total energy estimates. This work highlights the practical potential of variational quantum algorithms for studying complex molecular systems relevant to catalysis, hydrogen storage, and battery technologies.
Quantum computers hold significant promise for the efficient and accurate simulation of strongly correlated materials, including those critical to next-generation battery technologies. However, current quantum hardware is constrained by limited qubit counts and susceptibility to decoherence, making exact simulations of complex materials infeasible. In response, the Noisy Intermediate-Scale Quantum (NISQ) era has fostered the development of hybrid quantum-classical algorithms that can operate effectively within these limitations. In this work, we apply NISQ-compatible methods to investigate fundamental processes occurring inside battery systems, especially in organic electrode materials. A key aspect of our approach is the decomposition of these systems into active spaces - reduced regions that capture the most chemically relevant electrons and interactions. Within these active spaces, quantum algorithms are employed to resolve the electronic structure with high precision. By strategically focusing quantum computational resources where they are most impactful, our approach highlights the potential of quantum computing in advancing the fundamental understanding of battery materials - marking an early but significant step toward practical quantum simulations in energy storage research.
Accurately capturing electron correlation in large-scale molecular systems remains one of the foremost challenges in quantum chemistry and a primary driver for the development of quantum algorithms. Classical configuration-interaction methods, while rigorous, suffer from exponential scaling, rendering them impractical for large or strongly correlated systems. Overcoming this limitation is central to realizing the promise of quantum computing in chemistry. Here, we investigate the pyridine-Li ion complex using three quantum algorithms: the variational quantum eigensolver (VQE), the subspace quantum diagonalization (SQD) method, and the recently introduced handover iterative VQE (HI-VQE). Our results demonstrate how new generations of hybrid quantum-classical frameworks overcome the scalability and noise sensitivity that constrain conventional VQE approaches. SQD and HI-VQE achieve ground-state energy calculations for problem sizes inaccessible to classical computation, marking a clear advance toward quantum advantage. In particular, HI-VQE enables calculations within active spaces as large as (24e,22o), requiring 44 qubits-well beyond the reach of classical CASCI and VQE. This capability provides a systematic pathway for incorporating increasing numbers of electrons into quantum treatment, thereby approaching exact molecular energies. Importantly, both SQD and HI-VQE exhibit robustness against hardware noise, a critical improvement over earlier approaches. By enabling quantum simulations of molecular systems previously deemed intractable, SQD and HI-VQE offer a realistic route toward practical quantum advantage in computational chemistry. The comparison between HI-VQE and SQD shows that optimizing circuit parameters is crucial for accurate simulation.
Scientific simulations demand methods combining scalability with predictive accuracy. Density Functional Theory (DFT) on High-Performance Computing (HPC) enables large-scale electronic-structure simulations but is limited by approximations affecting strongly correlated systems and band-gap predictions. Quantum computing offers a pathway to address this, though current Noisy Intermediate-Scale Quantum (NISQ) hardware remains constrained by qubit resources, noise, and execution cost.
This work presents a hybrid DFT-Quantum Embedding (QDFT) framework integrating classical HPC-based DFT with a quantum electronic-structure solver. Large systems are partitioned to isolate a chemically relevant active space, treated via the Variational Quantum Eigensolver (VQE), while the remaining degrees of freedom are described by DFT. The framework incorporates active-space selection, embedded Hamiltonian construction, symmetry preservation, operator mapping, self-consistent density updating, and modular classical-quantum coupling.
We focus on noiseless quantum simulation to systematically evaluate accuracy, convergence, active-space dependence, computational cost, and HPC scalability without hardware noise. Detailed profiling identifies computational bottlenecks and highlights limitations of CPU-based quantum simulation. A QPU runtime-estimation methodology is additionally developed to assess execution requirements on actual quantum hardware.
Results demonstrate quantum embedding's potential to improve selected electronic-structure properties while retaining classical HPC's scalability. Noisy quantum simulation and QPU execution remain key future directions, providing a pathway toward practical, scalable HPC-quantum hybrid simulations as hardware matures.
Rapid progress in noisy intermediate-scale quantum (NISQ) computing technology has led to the development of novel resource-efficient hybrid quantum-classical algorithms, such as the variational quantum eigensolver (VQE), that can address open challenges in quantum chemistry, physics, and material science. Proof-of-principle quantum chemistry simulations for small molecules have been demonstrated on NISQ devices. While several approaches have been theoretically proposed for correlated materials, NISQ simulations of interacting periodic models on current quantum devices have not yet been demonstrated. Here, we develop a hybrid quantum-classical simulation framework for correlated electron systems based on the Gutzwiller variational embedding approach. We implement this framework on Rigetti quantum processing units (QPUs) and apply it to the periodic Anderson model, which describes a correlated heavy electron band hybridizing with noninteracting conduction electrons. Our simulation results quantitatively reproduce the known ground state quantum phase diagram including metallic, Kondo and Mott insulating phases. This is the first fully self-consistent hybrid quantum-classical simulation of an infinite correlated lattice model executed on QPUs, demonstrating that the Gutzwiller hybrid quantum-classical embedding framework is a powerful approach to simulate correlated materials on NISQ hardware. This benchmark study also puts forth a concrete pathway towards practical quantum advantage on NISQ devices.
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.
Embedding-based quantum simulations have emerged as a promising paradigm for bridging quantum and classical scales in complex chemical systems. As molecular processes span multiple spatial and temporal regimes—from localized electron correlation to mesoscale reactivity—traditional quantum chemistry and classical potentials often fail to describe these interactions with sufficient accuracy and scalability. This study explores hybrid embedding frameworks that integrate quantum subspace models, density functional embedding, and quantum many-body solvers within hierarchical multi-scale workflows. By partitioning chemically active regions and treating them with quantum processors while embedding them within larger classical environments, the approach improves accuracy in reaction barrier estimation, excited-state dynamics, and strongly correlated interactions. We evaluate state-of-the-art quantum embedding techniques, discuss advances in quantum resource allocation and error mitigation, and demonstrate how embedding can reduce computational depth while preserving chemically essential features. The study highlights key opportunities for developing next-generation quantum-enhanced multi-scale simulation pipelines capable of accelerating catalyst design, energy storage materials, and biochemical modeling.