Accuracy and Potential of Hardware-Efficient Ansätze for Molecular Ground and Excited State Electronic Structure Calculations: Benchmark and Analysis of High-Depth Quantum Circuits

The variational quantum eigensolver (VQE) algorithm has positioned quantum chemistry calculation methods as promising applications for noisy intermediate-scale quantum (NISQ) devices. In NISQ devices, where the quantum noise is considerable, it is desirable to have an ansatz for the quantum circuit that is practical to implement and capable of achieving high chemical accuracy. Hardware-efficient <i>Ansätze</i> (HEA), such as the RyRz linear ansatz (RLA) and its modified form that preserves physical quantitiesthe symmetry preserving ansatz (SPA)are constructed using quantum gates that can be implemented easily on a quantum computer. However, the extent to which HEA can accurately yield the electronic state energies of actual molecules and the number of quantum gates required to achieve chemical accuracywhich, in practical cases, should be within 1 kcal/mol of the exact energy valueare not well understood. In this study, we aimed to gain a detailed understanding of these aspects by performing noiseless simulations to obtain the ground and low-lying excited state using high-depth HEA quantum circuits for several molecules, including LiH, H₂O, BeH₂, CH₄, and N₂. From the results, we demonstrated that symmetry preserving HEA, such as SPA, can achieve accurate computational results that maintain CCSD-level chemical accuracy by increasing the number of layers. We quantitatively analyze how the expressibility and entangling capability of RLA and SPA quantum circuits evolve with circuit depth. Our results reveal that while increased layers generally expand accessible Hilbert space and entanglement, differences in their limitations highlight the importance of considering physically allowed entanglement for performance of a parametric quantum circuit in VQE. We also studied the potential energy surface of the dissociation of these molecules and found that quantum circuits using SPA can capture static electron correlation, which is challenging to address with classical single-reference quantum chemistry methods such as CCSD. These results from SPA demonstrate its potential to represent electronic states, as it achieves highly accurate results with fewer gate operations compared to physically inspired quantum circuits such as the Unitary Coupled Cluster (UCC) method. This study establishes a possible path for the application of quantum devices in solving quantum chemistry problems.