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

Simulation of molecular ground states on near-term quantum hardware is constrained by qubit availability and the cost of variational optimization. To address these challenges, the Subspace Restriction Scheme (SRS) is introduced as a mathematical framework that projects the molecular Hamiltonian onto a selected Fock subspace prior to qubit encoding. By enforcing molecular multiplicity and a generalized Hund's rule, the Multi-Hund Subspace (MHS) is constructed. This physically motivated restriction significantly reduces the effective Fock-space dimension, asymptotically saving $N$ qubits for a Hamiltonian of $M$ spatial orbitals and $N$ electrons. As a result, we successfully overcome classical memory bottlenecks and enable simulations of large systems, such as the $H_{22}$ chain, which requires 44 qubits under standard Jordan-Wigner (JW) encoding. While the strict pairing structure may limit accuracy in strongly correlated dissociation regimes, MHS effectively captures the essential low-energy physics of closed-shell molecules near equilibrium. In Variational Quantum Eigensolver (VQE) benchmarks, MHS enhances optimization behaviour and achieves high accuracy with a shallow ansatz. These findings demonstrate that physically motivated subspace restriction offers an effective approach to more resource-efficient quantum-chemistry simulations.