Hamiltonian truncation and quantum simulation of strong-field QED beyond tree level

Quantum electrodynamics in strong background fields provides an interesting class of problems for classical and quantum simulation. In this paper we formulate simulations of polarization (helicity) flip for a photon colliding with a high-intensity plane wave. Polarization flip is a one-loop effect, which requires addressing new issues that do not arise in simulations of tree-level processes. Working in the momentum-space Fock basis, while convenient for the extraction of scattering amplitudes, requires tuning counterterms to cancel large cutoff effects. We compute analytic formulas for the counterterms at one loop. We then construct circuits for quantum simulations of the process, perform noiseless simulations on classical computers to assess discretization errors, and discuss resource estimates for future simulations on quantum hardware.