Sample-based Quantum Diagonalization Enables Efficient LASSCF Calculations of Complex Molecules

Accurately modelling strongly correlated electronic systems presents a significant challenge in modern computational chemistry. Qiaohong Wang from the University of Chicago, Mario Motta from IBM Quantum, and Ruhee D’Cunha, alongside colleagues including Kevin J. Sung and Matthew R. Hermes, now demonstrate a new approach to overcome this limitation. Their research introduces a method called LASSQD, which combines sample-based quantum diagonalization with the localized active space self-consistent field method, offering a pathway to tackle complex systems previously beyond reach.

The team showcases that LASSQD not only handles larger fragment sizes than traditional methods, but also achieves comparable accuracy, delivering results within 1kcal/mol of existing techniques and providing a robust foundation for further refinement with perturbative treatments to capture a more complete picture of electronic correlation. The localized active space self-consistent field (LASSCF) method employs a product of fragment active spaces as a variational space, addressing the complexities of the Schrödinger equation. Quantum Computing for Iron Porphyrin Electronic Structure Research focuses on leveraging quantum computers and hybrid quantum-classical approaches to solve complex electronic structure problems. Scientists are exploring variational quantum algorithms to optimize electronic wavefunctions and utilizing quantum Monte Carlo methods to improve calculations. Techniques like dynamical decoupling and randomized compiling are being developed to mitigate noise and decoherence in quantum computations, and classical simulators are used to test algorithms before implementation on quantum hardware. Alongside these quantum approaches, established computational chemistry methods, including multi-reference configuration interaction, perturbation theory, and coupled cluster theory, remain crucial tools. A significant area of investigation centers on understanding the electronic structure of iron porphyrins, particularly the factors determining their spin state. Researchers are meticulously investigating spin state energetics and recognizing the importance of including both valence and semicore electrons in accurate calculations. These theoretical calculations are then validated by comparison to experimental data, such as Mössbauer and Raman spectroscopy. The overarching goal is to bridge the gap between quantum computing and chemistry, combining the strengths of both classical and quantum algorithms. Error mitigation is recognized as crucial for obtaining reliable results from current quantum hardware, and accurate treatment of electron correlation is paramount, especially in systems like iron porphyrins where it dictates the spin state. Computational cost remains a constant challenge, driving the development of algorithmic improvements and more efficient hardware. Selecting the appropriate active space, the set of orbitals included in the correlated calculation, is crucial for balancing accuracy and computational cost, and localized active space methods offer a promising approach. Key technologies and tools driving this research include IBM’s Qiskit quantum computing framework, the fast fermionic simulator ffsim, the sample-based quantum diagonalization solver LASSQD, and the Python-based quantum chemistry package PySCF.

This research represents an active and evolving field, with scientists developing and implementing quantum algorithms, applying them to challenging chemical systems, and pushing the boundaries of computational chemistry. LASSQD Enables Large-Scale Metal Complex Calculations Scientists have developed a new computational method, LASSQD, that significantly expands the scale of quantum chemical calculations for complex metallic systems. This work addresses a central challenge in computational chemistry: accurately describing the behavior of electrons in strongly correlated systems, which are notoriously difficult to model.

The team combined the localized active space self-consistent field (LASSCF) method with sample-based diagonalization (SQD) to create a more efficient approach for solving the electronic Schrödinger equation. The researchers successfully applied LASSQD to the [Fe(H₂O)₄]²bpym⁴⁺ compound and the [FeIIIFeIIIFeII(μ₃-O)-(HCOO)₆] complex, calculating their intermediate-spin ground state energies. Experiments revealed that LASSQD can handle fragment sizes previously intractable for LASSCF, achieving results within 1kcal/mol of the more computationally demanding LASSCF method. This level of accuracy is competitive with alternative classical methods used to solve the Schrödinger equation, establishing LASSQD as a viable starting point for more advanced perturbative treatments. A key innovation was the development of a “carryover” procedure to mitigate the stochasticity inherent in SQD, ensuring stable and reliable results during the self-consistent field orbital optimization process. Tests on the [Fe(H₂O)₄]²bpym⁴⁺ and [FeIIIFeIIIFeII(μ₃-O)-(HCOO)₆] complexes demonstrated that LASSQD efficiently approximates the full configuration interaction (FCI) space, even with the approximations introduced by SQD. Furthermore, the method was successfully applied to iron-porphyrin, a system with fragment sizes too large for classical FCI calculations, demonstrating its potential for tackling even more complex chemical systems. These results pave the way for utilizing near-term quantum devices as scalable active space solvers for multireference quantum chemistry, offering a framework for assessing the limitations and future potential of quantum hardware and software. LASSQD Achieves Accurate Electronic Structure Calculations This research presents a novel computational framework, LASSQD, which integrates approximate quantum solvers into a fragment-based approach for calculating the energies of strongly correlated electronic systems. By combining this method with localized active space self-consistent field (LASSCF) calculations, scientists have achieved a significant advancement in tackling complex chemical problems previously intractable with conventional methods. LASSQD successfully approximates the full configuration interaction (FCI) method, a highly accurate but computationally demanding technique, while maintaining accuracy within 1 kcal/mol of LASSCF, but using a fraction of the computational resources. The key innovation lies in adapting a carry-over strategy to the self-consistent field formulation, which reduces the impact of statistical fluctuations and ensures stable orbital optimization. Applications to bimetallic and trimetallic complexes demonstrate that LASSQD efficiently handles fragment sizes inaccessible to LASSCF, opening new avenues for studying complex chemical systems. The researchers acknowledge that the accuracy of the method is currently limited by the approximate quantum solvers employed, and future work will focus on improving these solvers through strategies such as generalized eigenvalue approaches and semi-stochastic sampling. Further development will also concentrate on extending LASSQD to accurately account for correlations between fragments, which is essential for understanding strongly coupled systems. These ongoing efforts position LASSQD as a promising and adaptable pathway for applying near-term quantum algorithms to large, strongly correlated systems, offering a powerful tool for advancing materials science and computational chemistry. 👉 More information🗞 Sample-based quantum diagonalization as parallel fragment solver for the localized active space self-consistent field method🧠 ArXiv: https://arxiv.org/abs/2512.14936 Tags: