Modern Approaches to Exact Diagonalization and Selected Configuration Interaction with the Adaptive Sampling CI Method

TLDR

Recent advances in selected CI, such as the adaptive sampling configuration interaction (ASCI) algorithm and its heat bath extension, have made ASCI competitive with the most accurate techniques for solving quantum Hamiltonians. This work demonstrates that efficient selected CI/exact diagonalization algorithms can be driven by fast sorting algorithms, analogous to how iterative diagonalization relies on matrix–vector multiplication. We introduce new algorithms for all stages of selected CI—including ASCI search, dynamic bit masking, fast orbital rotations, fast diagonal matrix elements, and residue arrays—and show their applicability to large systems with benchmark data from the G1 dataset. The resulting algorithms are fast, scalable, and outperform other approaches; they enable full‑CI simulations of systems such as Si₂H₆ (34 electrons, 152 orbitals) and support efficient deterministic perturbation theory using hash functions.

Abstract

Recent advances in selected CI, including the adaptive sampling configuration interaction (ASCI) algorithm and its heat bath extension, have made the ASCI approach competitive with the most accurate techniques available, and hence an increasingly powerful tool in solving quantum Hamiltonians. In this work, we show that a useful paradigm for generating efficient selected CI/exact diagonalization algorithms is driven by fast sorting algorithms, much in the same way iterative diagonalization is based on the paradigm of matrix vector multiplication. We present several new algorithms for all parts of performing a selected CI, which includes new ASCI search, dynamic bit masking, fast orbital rotations, fast diagonal matrix elements, and residue arrays. The algorithms presented here are fast and scalable, and we find that because they are built on fast sorting algorithms they are more efficient than all other approaches we considered. After introducing these techniques we present ASCI results applied to a large range of systems and basis sets in order to demonstrate the types of simulations that can be practically treated at the full-CI level with modern methods and hardware, presenting double- and triple-zeta benchmark data for the G1 dataset. The largest of these calculations is Si$_{2}$H$_{6}$ which is a simulation of 34 electrons in 152 orbitals. We also present some preliminary results for fast deterministic perturbation theory simulations that use hash functions to maintain high efficiency for treating large basis sets.