Molecular Ground State Simulation by Subspace Restriction and Hund's Rule

The Subspace Restriction Scheme (SRS) is presented to address the qubit and resource constraints of molecular simulation on near-term quantum hardware. SRS restricts a molecular Hamiltonian to a selected determinant subspace before qubit encoding, so a D-dimensional subspace requires only q= 2D qubits. We apply SRS to the established seniority-resolved Multi-Hund Subspaces MHS(Ω) and develop compact encodings for these sectors. At fixed seniority and filling fraction, MHS asymptotically uses about half as many qubits as a compact particle-conserving encoding. For the H 22 chain, the register shrinks from 44 to 20 qubits. Compression can nevertheless increase Pauli-operator density and does not always reduce measurement cost. In noiseless VQE benchmarks, shallow circuits reach within 1.6 mHa of the exact subspace minima using only 4 -- 30 CNOT gates. However, the corresponding subspace minima for LiH, HF, OH, and CH remain 4.39 -- 9.73 mHa above FCI. Full-space UCCSD reaches chemical accuracy but requires hundreds to thousands of CNOT gates. SRS therefore provides a controlled resource--accuracy trade-off when register width is the binding constraint and the target state is well represented within a selected seniority sector.