In this talk I will discuss ongoing progress in two projects. The first project is related to implementing the time-evolution operator corresponding to the Kogut-Susskind formulation of Lattice Gauge Theories (U(1), SU(2), and SU(3)), and an improvement thereof called the Loop-String-Hadron formulation. We give a simple, generic method of decomposing a Hamiltonian into a minimal sum of easily-diagonalizable summands, suitable to plug into Trotter- or Block-Encoding-based Hamiltonian simulation methods. For the SU(3) fermion-gauge interaction term, our method decreases the complexity by a factor of ~1/500 over prior art. I will also discuss major obstacles in giving feasible algorithms for quantum simulations of Lattice Gauge Theories, which I hope to address over the course of my PhD. The second project is about understanding how we could use quantum computers to learn excited eigenvalues of lattice nuclear theories. I will compare textbook phase estimation to recently-developed block-encoding-based methods, applied to a Chiral Effective Field Theory Hamiltonian.