An Iterative Dual-Channel Neural Quantum State Algorithm for Selected Configuration Interaction

Accurately solving the electronic Schr"{o}dinger equation for strongly correlated systems remains a central challenge in quantum chemistry, where the exponential growth of configuration space limits the applicability of exact methods. Selected Configuration Interaction (SCI) algorithms address this challenge by adaptively constructing compact determinantal expansions, yet their efficiency depends critically on the quality of the sampling strategy used to identify chemically important configurations. Here we introduce the Handover Iterative Neural Quantum State (HI-NQS) algorithm, which embeds a classically trained autoregressive Transformer neural quantum state within the iterative sample--diagonalize--update framework of Sample-Based Quantum Diagonalization. A dual-channel Transformer architecture with explicit spin-up/spin-down cross-attention encodes fermionic spin structure as an architectural inductive bias, enabling expressive and physically informed wavefunction representations. After each subspace diagonalization, the resulting eigenvector is distilled back into the network through a factorized spin-marginal teacher signal, establishing a closed feedback loop between generative sampling and exact diagonalization. Benchmarks across a range of small molecules and a systematic nitrogen active-space series demonstrate that HI-NQS achieves chemical accuracy on all systems tested, with determinant-count scaling substantially more favorable than conventional CIPSI-based SCI for all but the smallest active spaces. All calculations are performed on GPU hardware without quantum computing resources, establishing HI-NQS as an efficient and scalable purely classical approach to the selected configuration interaction problem.