Numerically Exact Configuration Interaction at Quadrillion-Determinant Scale

Abstract

The combinatorial scaling of configuration interaction (CI) has long restricted its applicability to only the simplest molecular systems. Here, we report the first numerically exact CI calculation exceeding one quadrillion ($10^{15}$) determinants, enabled by categorical compression within the small-tensor-product distributed active space (STP-DAS) framework. As a demonstration, we converged the relativistic complete active space CI (CASCI) ground state of HBrTe involving over $10^{15}$ complex-valued 2-spinor determinants in under 34.5 hours (time-to-completion) using 1000 nodes, representing the largest CASCI calculation reported to date. Additionally, we achieved $\mathbf{\sigma }$-build times of just 5 minutes for systems with approximately 150 billion complex-valued 2-spinor determinants using only a few compute nodes. Extensive benchmarks confirm that the method retains numerical exactness with drastically reduced resource demands. Compared to previous state-of-the-art CI calculations, this work represents a 3-orders-of-magnitude increase in CI space, a 6-orders-of-magnitude increase in FLOP count, and a 6-orders-of-magnitude improvement in computational speed. By introducing a numerically exact, categorically compressed representation of the CI expansion vectors and reformulating the $\mathbf{\sigma }$-build accordingly, we eliminate memory bottlenecks associated with storing excitation lists and CI vectors while significantly reducing computational cost. A compression-compatible preconditioner further enhances performance by generating compressed CI expansion vectors throughout Davidson iterations. This work establishes a new computational frontier for numerically exact CI methods, enabling chemically and physically accurate simulations of strongly correlated, spin-orbit coupled systems previously thought to be beyond reach.

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