  Hadronic vacuum polarization (HVP) and light-by-light scattering (HLBL) are
crucial for evaluating the Standard Model predictions concerning the muon's
anomalous magnetic moment. However, direct first-principle lattice gauge
theory-based calculations of these observables in the timelike region remain
challenging. Discrepancies persist between lattice quantum chromodynamics (QCD)
calculations in the spacelike region and dispersive approaches relying on
experimental data parametrization from the timelike region. Here, we introduce
a methodology employing 1+1-dimensional quantum electrodynamics (QED), i.e. the
Schwinger Model, to investigate the HVP and HLBL. To that end, we use both
tensor network techniques, specifically matrix product states, and classical
emulators of digital quantum computers. Demonstrating feasibility in a
simplified model, our approach sets the stage for future endeavors leveraging
digital quantum computers.
