Quantum computers can possibly help in the near future to simulate mole-cules and do electronic structure calculations. To work on the near term quantum devices the variational quantum eigensolver ...Show moreQuantum computers can possibly help in the near future to simulate mole-cules and do electronic structure calculations. To work on the near term quantum devices the variational quantum eigensolver (VQE) is an auspicious candidate and particularly the application of the unitary coupled-cluster singles and doubles ansatz. Despite the high accuracy the scaling in the number of terms is unfavourable making the circuit depth too large. In this thesis we look at a possible truncation scheme based on classical quantum chemistry methods to decrease the number of terms while preserving accurate ground state energies. This truncation is shown with numerical results for H$_4$ and N$_2$ giving a significantly reduced number of terms.Show less
To find solutions to systems of conservation laws with discontinuities, weak solutions will be studied. To pick a unique weak solution one requires some additional conditions. In this thesis we...Show moreTo find solutions to systems of conservation laws with discontinuities, weak solutions will be studied. To pick a unique weak solution one requires some additional conditions. In this thesis we will see that for the Riemann problem in one spatial dimension, the Lax entropy conditions are a way to do this. By considering the Euler equations we will see that these conditions are equivalent to the second law of thermodynamics and therefore pick the physically relevant solution. Furthermore, we construct numerical solutions to a specific Riemann problem using a standard discretization method and a method based on nonlinear shocks, followed by a on discussion their strengths and weaknesses.Show less
