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

TL;DR

This work extends the Handover-Iterative VQE (HI-VQE) framework to benchmark challenging strongly correlated systems, notably the nitrogen molecule N$_2$ and the Fe–S cluster. By coupling quantum-sampled configurations with classical subspace diagonalization, HI-VQE reproduces HCI-level energies within millihartree accuracy while using a substantially smaller determinant subspace, demonstrating favorable scalability on NISQ hardware. The results show HI-VQE effectively captures both dynamic and static correlation across bond dissociation and spin-coupled metal clusters, with tangible reductions in classical-diagonalization cost (scaling as $O(N^{3})$ in the subspace size). Overall, the study provides a viable quantum-assisted pathway for accurate electronic structure in bioinorganic and catalytic systems, moving toward practical quantum advantage as hardware improves.

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.

Figures (7)

• Figure 1: Overview of the HI-VQE iterative workflow. Each iteration uses QPU-sampled states with the current circuit parameters, optionally refines them via configuration recovery (CR)/tensor product (TP)/classical expansion (CE), and diagonalizes both the sampled and accumulated subspaces to update parameters and propagate the optimized state forward. The subspace extraction is optionally activated to carry on highly contributing states.
• Figure 2: Subspace expansion behavior of left) HI-VQE, and right) HCI
• Figure 3: Top: Potential energy surface of N2 cc-pVDZ calculated by RHF, HCI and HI-VQE. Bottom: HI-VQE energy error w.r.t. HCI $(\epsilon = 1\times 10^{-6})$
• Figure 4: N2 cc-pVDZ dissociation: subspace size comparison between HCI and HI-VQE.
• Figure 5: Top: Determinant scaling with qubit number comparison between CASCI, HI-VQE, and HCI methods for $N_2$ cc-pVDZ at bond distance 3.0 Å . Bottom: Absolute energy difference between HI-VQE and HCI.