Selected-CI Eigensolver
a preconditioned eigensolver for selected configuration interaction that does most of its work with cheap, approximate Hamiltonian products
collaborators: Prof. Phani Motamarri
Ongoing work.
Selected configuration interaction (selected CI) methods describe strongly correlated molecules by choosing a subset of the most important electronic configurations and finding the lowest energy of the Hamiltonian in the space they span. The configurations can be chosen by classical heuristics or sampled on a quantum computer, as in sample-based quantum diagonalization; either way, for the molecules of interest the subspace holds tens of millions of determinants or more. The diagonalization, dominated by repeated Hamiltonian-vector products on GPUs, then becomes the main cost.
This project develops an inverse-free preconditioned Krylov eigensolver for these subspace problems, implemented in SBD, RIKEN’s GPU diagonalization library for sample-based quantum diagonalization. Like our R-ChFSI eigensolver, it tolerates inexact products: most of the work is done with an inexpensive approximation to the Hamiltonian, while a few exact products keep the final energy at full accuracy. Together with faster GPU kernels for the exact Hamiltonian products, the solver reaches the same accuracy substantially faster than SBD’s default Davidson method on the largest subspaces we have tested, from small molecules to iron-sulfur clusters.
