Quantum Computing Advances Strongly Correlated Systems with Handover-Iterative VQE and SHCI Convergence

Accurately modelling strongly correlated electronic systems presents a significant hurdle in quantum chemistry, due to the complex interactions between electrons. Pilsun Yoo, Kyungmin Kim, and Eyuel E. Elala, all from Qunova Computing, Inc., alongside Shane McFarthing, Aidan Pellow, and Johanna I. Fuks, have advanced the Handover-Iterative Variational Quantum Eigensolver (HI-VQE) algorithm to address this challenge. Their research introduces a dynamic information exchange between quantum and classical computers, designed to function effectively on current Noisy Intermediate-Scale Quantum (NISQ) devices. This work benchmarks the extended HI-VQE against the nitrogen molecule and an iron-sulfur (Fe-S) cluster, providing stringent tests for electronic-structure methods and demonstrating a potential route towards simulating complex systems like bioinorganic molecules and correlated materials. By comparing results to Heat-bath Configuration Interaction (HCI) benchmarks, the team assesses the algorithm’s accuracy and scalability in capturing multireference correlation effects.

Researchers are exploring quantum computing algorithms to overcome this limitation by utilising entanglement and superposition for more efficient representation of correlated states. These systems are used as rigorous tests for both conventional and quantum electronic structure methods. Successful demonstration on these canonical systems suggests the viability of using quantum computing to simulate complex bioinorganic molecules, catalytic mechanisms, and correlated materials, areas currently limited by classical computational power. The study pioneered an iterative “handover” mechanism, enabling efficient computation by leveraging the strengths of both computational paradigms. These molecules were selected as prototypical examples of strongly correlated systems, serving as stringent tests for electronic-structure methods and highlighting distinct correlation challenges. The nitrogen molecule exemplifies bond dissociation and static correlation, while Fe-S clusters demonstrate multi-center spin coupling and charge delocalization, demanding a robust methodological approach. This method generates single and double excitations from a reference state, selecting determinants based on Hamiltonian matrix element thresholds exceeding a defined value ε. Scientists also harnessed the stochastic heat-bath configuration interaction (SHCI) method, combining deterministic determinant selection with stochastic perturbative corrections to further refine accuracy for active spaces exceeding 100 orbitals. Furthermore, the research incorporated tensor-network formalisms, specifically the Density Matrix Renormalization Group (DMRG), which reformulates the wavefunction as a matrix product state to efficiently capture localized entanglement. Specifically, the team demonstrated the ability to accurately model the dissociation of the nitrogen molecule, a benchmark for static correlation, and the multi-center spin coupling present in iron-sulfur clusters. The team generated stochastic heat-bath configuration interaction (SHCI) data, achieving sub-millihartree accuracy in variational spaces containing up to 10 20 determinants, establishing a high-precision benchmark for comparison. Measurements confirm the algorithm’s ability to handle active spaces exceeding 100 orbitals, a significant advancement in the field of quantum simulations. This iterative handover mechanism between quantum sampling and classical processing offers a scalable route for treating both localized and delocalized electron correlation. Future work will likely focus on applying this methodology to increasingly complex systems and exploring its potential with more advanced quantum hardware.