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

Abstract

Sample-based quantum diagonalization (SQD) is a hybrid quantum-classical algorithm for estimating ground-state energies in electronic-structure calculations. It uses a quantum processor as a sampler to construct a variational subspace, with Hamiltonian projection and diagonalization performed classically. A critical step in SQD is self-consistent particle-number recovery guided by a global reference occupancy vector. In strongly correlated systems, however, dominant determinants can be distributed across regions of determinant space, causing this reference to become mixture-averaged and biasing recovery toward mean occupations. Here, we introduce cluster-adaptive SQD (CSQD), which clusters pooled single-spin strings and performs particle-number recovery using cluster-specific reference occupancy vectors. Under a matched variational budget, CSQD lowers ground-state energies relative to SQD by up to 15.95 mHa for stretched N2 in a (10e,26o) active space and 57.82 mHa for [2Fe-2S] in a (30e,20o) active space. These results suggest that CSQD better captures dispersed occupation structure in strongly correlated systems.