In this thesis, we begin by reviewing some of the most important Hamiltonian simulation algorithms that are applied in simulation of quantum field theories. Then we focus on state preparation which has been the slowest subroutine in previously known algorithms. We present two distinct methods that improve upon prior results. The first method utilizes classical computational tools such as Density  Matrix Renormalization Group to produce an efficient quantum algorithm for simulating fermionic quantum field theories in 1+1 dimensions. The second method presented is a heuristic algorithm that can prepare the vacuum of fermionic systems in more general cases and more efficiently than previous methods. With our last method, state preparation is no longer the bottleneck, as its runtime has the same asymptotic scaling with the desired precision as the remainder of the simulation algorithm. We then numerically demonstrate the effectiveness of this last method for the 1+1 dimensional Gross-Neveu model.