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

TL;DR

This paper extends the Handover-Iterative VQE algorithm to accurately simulate strongly correlated systems like N2 and Fe-S clusters, demonstrating its potential for quantum chemistry applications on NISQ devices.

Contribution

The work introduces an extended HI-VQE method capable of benchmarking challenging strongly correlated molecules, showing promising accuracy and scalability on NISQ hardware.

Findings

Achieved quantitative agreement with classical HCI benchmarks.

Successfully captured multireference correlation effects.

Demonstrated viability for complex bioinorganic molecules.

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.