Connecting ansatz design to density functional observables using weighted subspace search vqe for kohn-sham hamiltonian
Ira Iryanti, Jun Hao Hue, Qidir Maulana Binu Soesanto, Muhammad Yusrul Hanna, Choirun Nisaa Rangkuti, L. C. Kwek, Yanoar Pribadi Sarwono · Physica Scripta · 2025
Abstract The use of the variational quantum eigensolver (VQE) on near-term quantum computers for solving Kohn–Sham Hamiltonian is still underexplored. In this study, we apply the weighted subspace search variational quantum eigensolver (weighted SSVQE) to obtain the occupied KS orbitals, their corresponding energies, and the total energy, exploring the effects of varying entanglement unitary blocks, circuit depths, and optimization strategies. While the choice of optimization algorithm has minimal impact on the total energy, it significantly influences convergence behavior, stability, and computational time. Our results further reveal the existence of an optimal weight configuration that achieves both faster convergence and improved energy accuracy. Furthermore, our findings highlight the critical role of ansatz depth and entanglement unitary blocks on total energy calculations across molecular geometries. The most effective design begins with a low-expressibility, low-entangling ansatz, such as linear entanglement unitary blocks, and repeats it until a sufficient number of layers is achieved. Using homoatomic and heteroatomic molecule as test sets, the approach remains valid and effective across systems exhibiting different types of electron correlation. This approach proves highly efficient, enabling shallow circuits that avoid convergence issues and closely match standard density functional calculations. This work thus offers a design strategy for shallow, convergence-friendly VQE circuits that match standard density functional energies.