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arXiv:2601.06935

Extending the Handover-Iterative VQE to Challenging Strongly Correlated Systems: $N_2$ and Fe-S Cluster

Pilsun Yoo, Kyungmin Kim, Eyuel E. Elala, Shane McFarthing, Aidan Pellow, Johanna I. Fuks, Doo Hyung Kang, Pratanphorn Nakliang, Jaewan Kim, Himadri Pathak, Tomonori Shirakawa, Seiji Yunoki, June-Koo Kevin Rhee

quant-phSubmitted Jan 11, 2026• Announced Jan 13, 2026• 0 citations
v1 · Jan 11, 2026v2 · Sep 12, 2026
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Abstract

Accurately describing strongly correlated electronic systems remains a central challenge in quantum chemistry, as electron-electron interactions give rise to complex many-body wavefunctions that are difficult to capture with conventional approximations. Classical wavefunction-based approaches, such as the Semistochastic Heat-bath Configuration Interaction (SHCI) and the Density Matrix Renormalization Group (DMRG), currently define the state of the art, systematically converging toward the Full Configuration Interaction (FCI) limit, but at a rapidly increasing computational cost. Quantum computing algorithms promise to alleviate this scaling bottleneck by leveraging entanglement and superposition to represent correlated states more compactly. We introduced the Handover-Iterative Variational Quantum Eigensolver (HI-VQE) as a practical quantum computing algorithm with an iterative "handover" mechanism that dynamically exchanges information between quantum and classical computers, even using Noisy Intermediate-Scale Quantum (NISQ) computers. In this work, we extend the HI-VQE to benchmark two prototypical strongly correlated systems, the nitrogen molecule $N_2$ and iron-sulfur (Fe-S) cluster, which serve as stringent tests for both classical and quantum electronic-structure methods. By comparing HI-VQE results against Heat-bath Configuration Interaction (HCI) benchmarks, we assess its accuracy, scalability, and ability to capture multireference correlation effects. Achieving quantitative agreement on these canonical systems demonstrates a viable pathway toward quantum-enhanced simulations of complex bioinorganic molecules, catalytic mechanisms, and correlated materials.

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Extending the Handover-Iterative VQE to Challenging Strongly Correlated Systems: N2N_2N2​ and Fe-S Cluster
Accurately describing strongly correlated electronic systems remains a central challenge in quantum chemistry, as electron-electron interactions give rise to complex many-body wavefunctions that are difficult to capture with conventional approximations. Classical wavefunction-based approaches, such as the Semistochastic Heat-bath Configuration Interaction (SHCI) and the Density Matrix Renormalization Group (DMRG), currently define the state of the art, systematically converging toward the Full Configuration Interaction (FCI) limit, but at a rapidly increasing computational cost. Quantum computing algorithms promise to alleviate this scaling bottleneck by leveraging entanglement and superposition to represent correlated states more compactly. We introduced the Handover-Iterative Variational Quantum Eigensolver (HI-VQE) as a practical quantum computing algorithm with an iterative "handover" mechanism that dynamically exchanges information between quantum and classical computers, even using Noisy Intermediate-Scale Quantum (NISQ) computers. In this work, we extend the HI-VQE to benchmark two prototypical strongly correlated systems, the nitrogen molecule N2N_2N2​ and iron-sulfur (Fe-S) cluster, which serve as stringent tests for both classical and quantum electronic-structure methods. By comparing HI-VQE results against Heat-bath Configuration Interaction (HCI) benchmarks, we assess its accuracy, scalability, and ability to capture multireference correlation effects. Achieving quantitative agreement on these canonical systems demonstrates a viable pathway toward quantum-enhanced simulations of complex bioinorganic molecules, catalytic mechanisms, and correlated materials.
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.
Accurately solving the electronic Schrödinger equation for strongly correlated systems remains a central challenge in quantum chemistry, where the exponential growth of configuration space limits the applicability of exact methods. Selected Configuration Interaction (SCI) algorithms address this challenge by adaptively constructing compact determinantal expansions, yet their efficiency depends critically on the quality of the sampling strategy used to identify chemically important configurations. Here we introduce the Handover Iterative Neural Quantum State (HI-NQS) algorithm, which embeds a classically trained autoregressive Transformer neural quantum state within the iterative sample--diagonalize--update framework of Sample-Based Quantum Diagonalization. A dual-channel Transformer architecture with explicit spin-up/spin-down cross-attention encodes fermionic spin structure as an architectural inductive bias, enabling expressive and physically informed wavefunction representations. After each subspace diagonalization, the resulting eigenvector is distilled back into the network through a factorized spin-marginal teacher signal, establishing a closed feedback loop between generative sampling and exact diagonalization. Benchmarks across a range of small molecules and a systematic nitrogen active-space series demonstrate that HI-NQS achieves chemical accuracy on all systems tested, with determinant-count scaling substantially more favorable than conventional CIPSI-based SCI for all but the smallest active spaces. All calculations are performed on GPU hardware without quantum computing resources, establishing HI-NQS as an efficient and scalable purely classical approach to the selected configuration interaction problem.
We present high-precision quantum computing simulations of three-body atoms (He, H−^-−) and molecules (H2+_2^+2+​, HD+^++), the latter being studied beyond the Born-Oppenheimer approximation. The Non-Iterative Disentangled Unitary Coupled Cluster Variational Quantum Eigensolver (NI-DUCC-VQE) [M. Haidar et al., Quantum Sci. Technol. 10, 025031 (2025)] is used. By combining a first-quantized Hamiltonian with a Minimal Complete Pool (MCP) of Lie-algebraic excitations, we construct a compact ansatz with a gradient-independent construction, avoiding costly gradient evaluations and yielding efficient computational scaling with both basis size and electron number. It avoids barren plateaus and enables rapid convergence, achieving energy errors as low as 10−11^{-11}−11 a.u. with state fidelities only limited by arithmetic precision in only a few thousand function evaluations in all four systems. These results make three-body atoms and molecules excellent candidates for benchmarking and testing on current Noisy Intermediate-Scale Quantum (NISQ) devices. Further, our approach can be extended to more complex systems with larger basis sets, taking advantage of the efficient scaling of qubit requirements to study electronic correlations and non-adiabatic effects with high precision. We also demonstrate the applicability of NI-DUCC-VQE for simulating higher-order effects such as relativistic corrections and hyperfine interactions.
Classical simulation of molecular electronic structure is often limited by the rapid increase in computational cost associated with describing electron correlation. The Variational Quantum Eigensolver (VQE) is one hybrid quantum-classical approach ideally adapted to the Noisy Intermediate-Scale Quantum (NISQ) regime. This work applies the VQE algorithm to compute ground state energies of a set of molecules:H2,H3+,LiH,HF,OH−,H2O,BH3,CH4\mathrm{H}_{2}, \mathrm{H}_{3}^{+}, \text{LiH}, \text{HF}, \text{OH}^{-}, \mathrm{H}_{2} \mathrm{O}, \text{BH}_{3}, \text{CH}_{4}H2​,H3+​,LiH,HF,OH−,H2​O,BH3​,CH4​, andNH3\text{NH}_{3}NH3​. The approach utilizes the Unitary Coupled Cluster for Single and Double excitations (UCCSD) ansatz along with the Bravyi-Kitaev transformation for fermionic-to-qubit encoding. Quantum simulation outputs are systematically benchmarked against Full Configuration Interaction (FCI), a numerically exact traditional approach, and Unrestricted Hartree-Fock (UHF). The results establish a robust consistency of the VQE-obtained molecular ground state energies against standard FCI and UHF benchmarks. This research provides a critical benchmark, confirming that VQE has the capability for high-precision molecular simulations and playing the role of a pivotal stepping stone toward revolutionizing applications in drug discovery and materials science.
Quantum computation offers a promising path towards efficient calculations of the electronic structure of correlated materials. The properties of iron-based materials, which are key for advancing geological and astrophysical understanding, are notoriously difficult to calculate with classical computers. However, despite the many recent advances in quantum computing on near intermediate scale quantum hardware, a full treatment of the electronic structure of high-ZZZ atoms or molecules remains challenging. Here, we investigate the ground-state properties of molecular FeO and Fe2_22​O2_22​ model Hamiltonians using classical exact diagonalization, Variational Quantum Eigensolver (VQE), and Sample-based Quantum Diagonalization (SQD). The experimental quintet ground state of FeO is recovered classically and with quantum algorithms, while a nonet ground state is recovered for Fe2_22​O2_22​. Although raw VQE does not achieve chemical accuracy for the ground state of FeO or Fe2_22​O2_22​, SQD with two connectivity shells recovers the exact ground energy for both molecules utilizing remarkably few quantum computational resources. Overall, our results indicate that ab  initioab \; initioabinitio-informed low-energy models of correlated materials, combined with SQD, offer a new alternative for scaling up calculations of ground-state properties of strongly correlated solids on existing quantum hardware.
The advancement of computational chemistry is currently stalled by the exponential memory scaling required to simulate strongly correlated electron systems on classical supercomputers. This fundamental barrier significantly impedes the rational design of complex pharmaceuticals and next-generation catalytic materials. This research aims to rigorously validate the immediate utility of Noisy Intermediate-Scale Quantum (NISQ) processors, demonstrating that “Quantum Advantage” has shifted from a theoretical milestone to a practical industrial reality. We employed a comparative research design utilizing the Variational Quantum Eigensolver (VQE) algorithm on the IBM Eagle quantum processor. The study targeted the electronic structure of iron-sulfur clusters and KRAS-G12C inhibitor binding sites, benchmarking quantum outputs against classical Density Functional Theory (DFT) and Full Configuration Interaction (FCI) standards, utilizing Zero-Noise Extrapolation for error mitigation. Results indicate that quantum simulations achieved chemical accuracy (within 1.6 kcal/mol) for these complex systems, whereas classical methods failed with deviations exceeding 8 kcal/mol. The data confirms that quantum hardware can now resolve electronic correlations invisible to classical approximation. We conclude that quantum computing offers a tangible, immediate pathway to accelerate discovery cycles in drug development and material science, necessitating the integration of hybrid quantum workflows into modern R&D pipelines.