Downfolding the Molecular Hamiltonian Matrix using Quantum Community Detection

Abstract: Calculating the ground state energy of a molecule efficiently is of great interest in quantum chemistry. The exact numerical solution of the electronic Schrodinger equation remains unfeasible for most molecules requiring approximate methods at best. In this paper we introduce the use of Quantum Community Detection performed using the D-Wave quantum annealer to reduce the molecular Hamiltonian matrix without chemical knowledge. Given a molecule represented by a matrix of Slater determinants, the connectivity between Slater determinants is viewed as a graph adjacency matrix for determining multiple communities based on modularity maximization. The resulting lowest energy cluster of Slater determinants is used to calculate the ground state energy within chemical accuracy. The details of this method are described along with demonstrating its performance across multiple molecules of interest and a bond dissociation example. This approach is general and can be used as part of electronic structure calculations to reduce the computation required.