SQD-Enabled Circuit Compression for Resource-Efficient Quantum Chemistry

Subspace Quantum Diagonalization (SQD) recovers ground-state energies by classically diagonalizing a Hamiltonian in the subspace spanned by quantum samples, requiring only bitstrings with sufficient ground-state overlap rather than an accurate variational energy. We reveal and exploit this underexplored robustness property: how much non-Clifford and variational expressivity can be removed from the sampling circuit before SQD accuracy degrades? We answer through two complementary compression techniques: gradient-based operator pruning, which discards low-impact excitation operators, and Clifford rounding, which snaps remaining parameters to the nearest Clifford angle. Both of these techniques can be applied to a VQE ansatz on a qubit-reduced Hamiltonian. A systematic ablation study across 21 molecules shows that median SQD error stays within chemical accuracy even at 50\% compression on both axes, while simulation speedup reaches $33\times$. Hardware validation on 6 molecules on IBM quantum hardware confirms up to $2.8\times$ transpiled-depth reduction with zero loss in SQD accuracy.