This thesis implements an algorithm for simulating electronic structure hamiltonians on quantum computers with linear architecture. An optimal swap network together with fermionic swap gates is used to implement a Trotter step in a curcuit of depth N (N being the number of spin orbitals). Additionally the two body interaction term is aproximated, accurate to within a desired tolerance ε. For this approximation a combination of a Chelsky decomposition and an eigenvalue decomposition is used.
For state preperation a QR decomposition scheme is used to diagonalize the molecular coefficient matrix using parallel givens rotations. With this algorithm arbitrary slater determinants can be prepared in depth N/2.