Efficient Ground State Estimation Using Generalized Hund's Rule

Quantum computers offer a promising approach to simulate the ground state of molecules, which is crucial for understanding molecular properties and chemical reactions. However, the limited number of available qubits on current devices poses a challenge for simulation. This paper investigates the feasibility of reducing the qubit usage of molecular simulation by examining specific fermionic states according to Hund's rule. We introduced a new framework based on qubit efficiency encoding. Based on this framework, the Hamiltonian is restricted to the Hund subspace. Compared to only concerned particle conservation, the proposed method can reduce N qubit usage for an M orbitals and N electrons molecule when M N. Additionally, when using the STO-3G basis sets, the simulations of the 15 molecules with given molecular geometry by the proposed method are close to the full configuration interaction. The absolute difference is at most 0. 121\%. Meanwhile, predictions from potential energy surfaces using the proposed method have an absolute difference at most 4. 1\%.