Enhancing initial state overlap through orbital optimization

Quantum phase estimation (PE) and its multiple variants require the efficient preparation of a state with high overlap with the targeted eigenstate. A few works were devoted to this task, notably introducing quantum circuits for preparing a configuration state function (CSF) instead of a single Slater determinant (SD) [2, 3, 4]. However, Lee et al. [1] showed that the overlap between a density matrix renormalization group approximation of the ground state and a single CSF (or SD) can be extremely small, thereby compromising the success of PE protocols. In addition, the overlap was shown to decrease exponentially on the studied iron-sulfur cluster molecules ranging from 2 to 8 metal centers including the sought-after FeMo cofactor. However, these single configuration states are defined in fixed orbital bases and orbital relaxation could improve their overlap with the ground state [1, 5]. Our work aims to show that this is indeed the case for classically demanding molecules. In this talk, I will introduce our comprehensive framework for orbital optimization and explore its implications for addressing the initial state overlap problem.

[1]  Seunghoon Lee, et al. Nature Communications, 14(1):1952, 2023.

[2]  Alessandro Carbone, et al. Symmetry, 14(3):624, 2022.

[3]  Kenji Sugisaki, et al. The Journal of Physical Chemistry A, 120(32):6459–6466, 2016.

[4]  Kenji Sugisaki, et al. Chemical Physics Letters, 737:100002, 2019.

[5] Norm M Tubman, et al. arXiv preprint arXiv:1809.05523, 2018.