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

Abstract

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 $q=\lceil {\log }_{2}D\rceil$ qubits. We apply SRS to the established seniority-resolved Multi-Hund Subspaces $\mathrm{MHS}(\Omega )$ 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 ${\mathrm{H}}_{22}$ 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.