Quantum-Centric Study of Methylene Singlet and Triplet States

This study explores the electronic structure of the CH$_2$ molecule, modeled as a (6e, 23o) system using a 52-qubit quantum experiment, which is relevant for interstellar and combustion chemistry. We focused on calculating the dissociation energies for CH$_2$ in the ground state triplet and the first excited state singlet, applying the Sample-based Quantum Diagonalization (SQD) method within a quantum-centric supercomputing framework. We evaluated the ability of SQD to provide accurate results compared to Selected Configuration Interaction (SCI) calculations and experimental values for the singlet-triplet gap. To our knowledge, this is the first study of an open-shell system, such as the CH$_2$ triplet, using SQD. To obtain accurate energy values, we implemented post-SQD orbital optimization and employed a warm-start approach using previously converged states. While the results for the singlet state dissociation were only a few milli-Hartrees from the SCI reference values, the triplet state exhibited greater variability. This discrepancy likely arises from differences in bit-string handling within the SQD method for open- versus closed-shell systems, as well as the inherently complex wavefunction character of the triplet state. The SQD-calculated singlet-triplet energy gap matched well with experimental and SCI values. This study enhances our understanding of the SQD method for open-shell systems and lays the groundwork for future applications in large-scale electronic structure studies using quantum algorithms.