Numerically exact configuration interaction at quadrillion-determinant scale

The combinatorial growth of configuration interaction (CI) has long limited this formally exact quantum chemistry method to only the smallest molecules. Here, we report a numerically exact CI calculation exceeding one quadrillion (10¹⁵) determinants, made possible by a lossless categorical compression strategy within the small-tensor-product distributed active space (STP-DAS) framework. This approach overcomes the traditional memory bottlenecks of CI by a numerically exact compression of the wavefunction representation and reformulating the most computationally demanding matrix-vector operations. Using this method, we performed a fully relativistic CI calculation of the ground state of HBrTe with over 10¹⁵ complex-valued determinants in just 34.5 h on 1000 computing nodes-the largest CI calculation ever reported. We further achieved fast computation for systems with hundreds of billions of determinants on only a few compute nodes. Extensive benchmarks confirm that the method retains full numerical exactness while cutting memory and computational cost by orders of magnitude. Compared to previous state-of-the-art CI calculations, this work achieves a 1000 times increase in CI space, a 10⁶-fold increase in floating-point operations performed, and a 10⁶-fold improvement in computational speed.