Selected Configuration Interaction Using Time-Evolved Population Statistics

Selected Configuration Interaction (SCI) is a method in molecular electronic structure theory that allows for the construction of configuration subspaces adapted to the particular system under study. This adaptability is achieved by guiding subspace construction with respect to a selection criterion designed to identify and retain the most important configurations for an accurate description of the system. Quantum-SCI (QSCI) introduces quantum resources to inform the construction of these subspaces, motivated by the classical hardness of state sampling and system dynamics. As with conventional SCI, the CI routine is still performed classically and is therefore not corrupted by hardware noise; only the subspace quality is affected by deficiencies in the quantum hardware. Previous QSCI approaches take the measurements produced by a physically motivated circuit construction, often with a recovery step to mitigate against errors, and form a subspace from the resulting configurations. We propose an alternative approach that is more aligned with conventional selection criteria but attempts to inject classically inaccessible information into the selection step with the aim of enabling new subspace expansion pathways. The approach presented in this work uses the population statistics of a time-evolved quantum state to predict likely single and double excitations away from existing configurations to bias the subspace expansion procedure. Importantly, this occupancy-guided expansion complements rather than replaces the direct inclusion of valid configurations sampled from the time-evolved quantum state, so determinants containing higher-order excitations can still enter the variational space in a single iteration. We also include multireference perturbation theory to capture missed correlations outside the configuration subspace. This is demonstrated on hardware by using 42 qubits of an IQM superconducting device to compute the potential energy curve of SiH4 in a 6-31G basis set as the Si–H bonds are stretched. We benchmark against the best-in-class Heatbath CI algorithm to assess the compactness of the resulting wave function.