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

Abstract: Molecular ground state simulation is a promising application of quantum computing. Nevertheless, this question has been shown as a QMA-complete problem, indicating that its complexity increases with the size of the molecule. To address this challenge, we focus on reducing the computation cost of molecular ground state simulation. In this study, we present a mathematical framework named Subspace Restriction Scheme (SRS), based on the Qubit Efficiency Encoding (QEE) method. Within this framework, we introduce and test a novel subspace, Multiplicity Hund Subspace (MH), which is generated by Hund's rule and selected based on molecular multiplicity. Our testing data and mathematical proofs demonstrate that MH subspace significantly reduces qubit usage compared to the classic Multiplicity Subspace and Particle Conservation Subspace (PC). For example, the ground state simulation of 10 electrons in 50 orbitals only requires 35 qubits, compared to the 44 qubits by PC and 100 qubits by the Jordan-Wigner transform. Furthermore, leveraging the reduced computation cost, we examine SRS for seldom tested larger molecules such as $\mathrm{CH}{4}$ and $\mathrm{H{2}O_{2}}$ without frozen any orbital and find that the MH subspace has less ground-state energy difference in the tested 15 molecules compared to PC subspace.