  We apply the Basis Light-Front Quantization (BLFQ) approach to the
Hamiltonian field theory of Quantum Electrodynamics (QED) in free space. We
solve for the mass eigenstates corresponding to an electron interacting with a
single photon in light-front gauge. Based on the resulting non-perturbative
ground state light-front amplitude we evaluate the electron anomalous magnetic
moment. The numerical results from extrapolating to the infinite basis limit
reproduce the perturbative Schwinger result with relative deviation less than
0.6%. We report significant improvements over previous works including the
development of analytic methods for evaluating the vertex matrix elements of
QED.
