Quantum Chromodynamics (QCD) is a fundamental theory of the strong interaction. At short distance, due to asymptotic freedom, the perturbative calculation is successful. However, when the coupling constant becomes larger, the perturbative calculation fails and the suitable

method must be found. Hamiltonian light-front quantum field theory constitutes a framework for the non-perturbative solution of invariant masses and correlated parton amplitudes of self bound systems.

By choosing the light-front gauge and adopting a basis function representation, we obtain a large, sparse, Hamiltonian matrix for mass eigenstates of gauge theories. Full covariance is recovered in the continuum limit, the inynite matrix limit. There is considerable freedom in the choice of the orthonormal and complete set of basis functions with convenience and convergence rates providing key considerations. In this thesis we use a two-dimensional harmonic oscillator basis for transverse modes that corresponds with eigensolutions of the soft-wall AdS/QCD model obtained from light-front holography. We outline our approach, present illustrative features of some non-interacting systems in a cavity and discuss the computational challenges.