Sample-based quantum diagonalization as parallel fragment solver for the localized active space self-consistent field method

TL;DR

This paper introduces LASSQD, a quantum-assisted method that uses sample-based quantum diagonalization to efficiently solve fragment Schrödinger equations in the LASSCF framework, enabling accurate treatment of strongly correlated systems.

Contribution

The paper presents LASSQD, a novel hybrid quantum-classical approach that overcomes computational bottlenecks in LASSCF by employing quantum sampling for fragment solutions.

Findings

LASSQD can handle larger fragment sizes than traditional LASSCF.

LASSQD achieves energy accuracy within 1 kcal/mol of LASSCF.

The method is competitive with classical quantum chemistry approaches.

Abstract

Accurately and efficiently describing strongly correlated electronic systems is a central challenge in quantum computational chemistry, with classical and quantum computers. The localized active space self-consistent field method (LASSCF) uses a product of fragment active spaces as a variational space, with the Schr\"odinger equation solved exactly in each fragment and the fragment active-space orbitals defined in a self-consistent manner. LASSCF is accurate for systems with strong intra-fragment and weak inter-fragment correlation, and its computational cost is combinatorial with respect to the size of the individual fragment active spaces, rather than their product. However, exactly solving the Schr\"odinger equation in each fragment remains a substantial bottleneck. Here, we address the possibility of solving the fragment active space Schr\"odinger equation with approximate methods, particularly sample-based quantum diagonalization (SQD). SQD is a technique that uses a quantum computer to sample configurations from a chemically motivated quantum circuit and a classical computer to mitigate errors and solve the Schr\"odinger equation in a subspace of the configuration space. We apply the proposed method, LASSQD, to the [Fe(H$_2$O)$_4$]$_2$bpym$^{4+}$ compound and the [Fe$^{\mathrm{III}}$Fe$^{\mathrm{III}}$Fe$^{\mathrm{II}}$($\mu$$_3$-O)-(HCOO)$_6$] complex for calculating the intermediate-spin ground state energies. We observe that LASSQD can tackle fragment sizes intractable by LASSCF, achieves within 1kcal/mol agreement to LASSCF, and delivers results that are competitive with alternative classical methods to solve the Schr\"odinger equation, and thus can be used as a starting point for a perturbative treatment (LASSQD-PDFT) to recover correlation external to the active space.