From Wavefunction Sparsity to Quantum Filter-Assisted Subspace Diagonalization

Subspace diagonalization techniques based on quantum sampling, such as quantum selected configuration interaction (QSCI) and sample-based quantum diagonalization (SQD), are a class of quantum-centric algorithms for approximating ground-state energies of many-body systems. One of the foundational bottlenecks for SQD is due to the lack of compactness of the ground-state wavefunctions. In this talk, we will introduce a filter-assisted SQD protocol that enhances the wavefunction sparsity through a quantum-circuit transformation of the Hamiltonian. Using the Gini coefficient as a robust sparsity measure, we clarify how sparsity determines the resource requirements of SQD. To construct the quantum filter, we develop a tensor-network-based automatic circuit-encoding algorithm that encodes the target matrix product states with controllable fidelity. We benchmark the method on the quantum Ising model under the transverse and longitudinal fields, using both numerical simulations and experiments on IBM quantum hardware. Our results show that the filter-assisted protocol reduces energy-estimation errors by orders of magnitude and substantially lowers the overhead of measurement compared with standard SQD, which highlight the potential of filter-assisted protocol in quantum-centric computing for strongly correlated materials.