Impact of the structure of the wave-function ansatz on accuracy and performance of quantum-chemistry calculations on Quantum Computers

The Variational Quantum Eigensolver (VQE) is a hybrid quantum-classical algorithm for near-term quantum computers. It offers an approach to solving central problems in quantum chemistry, such as estimating molecular ground-state energies by creating a parametrized trial wavefunction or ansatz state and iteratively updating the parameters using classical optimization to minimize the energy expectation value. A critical challenge in VQE implementation arises from the non-commutativity of operators in the ansatz circuit, constructed using first-order Suzuki-Trotter expansions. The underlying operator order significantly impacts the performance of VQE calculations. In this thesis, we systematically investigate the effects of the operator order of the first-order Trotterization of the Unitary Coupled Cluster on VQE performance for different molecules. Using numerical simulations, we demonstrate that arbitrarily chosen orders can lead to substantial variations in convergence behavior and inaccurate ground-state energy estimation. Furthermore, we attempt to evaluate ordering strategies based on the Hamiltonian to test the possibility of using a predecided order strategy. Our studies show that no discernible ordering strategy emerges based on the Hamiltonian and specific random orders perform significantly better than others.