Variational quantum simulations for determining the ground state of molecules in a globally-driven Rydberg platform

With the advent of the current era of Noisy Intermediate-Scale Quantum (NISQ) devices, new computational paradigms are being explored to leverage the developing quantum technologies. Hybrid quantum-classical algorithms, such as the variational quantum eigensolver or the variational quantum simulation, have emerged as a promising tool, for example, to accurately determine properties of molecules on a quantum computer or a quantum simulator, respectively. This is done by combining a quantum device with classical optimization. In this thesis, we propose a novel method for the variational preparation of ground states of Hermitian operators on a globally-driven Rydberg atom simulator. This novel method is based on a dynamical-Lie-algebra ansatz combined with an adaptive construction of the pulse sequence. When using our method to determine the ground state of molecules in numerical simulations, it outperforms a brute-force ansatz and shows clear advantages with respect to the dCRAB algorithm of quantum optimal control regarding the number of free parameters and expectation-value evaluations. In particular, we introduce an effective dynamical Lie algebra to avoid the calculation of the full dynamical Lie algebra, which is computationally intractable for larger systems. We also devise and implement a versatile toolkit to assess the reachability of the ground state of molecules and apply this toolkit prior to applying the variational quantum simulation. The method proposed is applicable to simulators beyond the Rydberg-atom architecture and to quantum computers.