Cluster-Adaptive Sample-Based Quantum Diagonalization for Strongly Correlated Systems

Abstract: Strongly correlated electronic systems exhibit inherently multiconfigurational wave functions, making it difficult to construct compact variational subspaces that preserve the essential multireference character. Quantum computing has emerged as a promising route to alleviate these limitations, and sample-based quantum diagonalization (SQD) is a representative hybrid approach that uses quantum hardware as a determinant sampler followed by classical diagonalization in the projected subspace. To mitigate hardware noise, SQD employs a self-consistent particle-number recovery guided by a single global reference occupancy vector. However, in strongly correlated, multimodal regimes, this global reference can become mixture-averaged and bias recovery toward a mean pattern, diluting mode-specific occupation structure and degrading the determinant pool. Here, we introduce cluster-adaptive SQD (CSQD), which clusters measurement samples via unsupervised learning and performs particle-number recovery using cluster-specific, self-consistently updated reference occupancy vectors. Under a matched variational budget, we benchmarked CSQD against SQD for N2 dissociation in a (10e,26o) active space and the [2Fe-2S] cluster in a (30e,20o) active space. Our results indicate that CSQD offers an advantage over SQD in estimating the ground-state energy in the strongly correlated regime, lowering the variational estimate by up to 15.95 mHa for stretched N2 and up to 45.53 mHa for [2Fe-2S], with modest additional classical overhead.