  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 that is solvable by adapting the ab initio
no-core methods of nuclear many-body theory. Full covariance is recovered in
the continuum limit, the infinite 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. Here, 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 and present illustrative features of some
non-interacting systems in a cavity. We illustrate the first steps towards
solving QED by obtaining the mass eigenstates of an electron in a cavity in
small basis spaces and discuss the computational challenges.
