Quantum computation of scattering amplitudes in scalar quantum electrodynamics

We present a quantum algorithm for the calculation of scattering amplitudes of massive charged scalar particles in scalar quantum electrodynamics. Our algorithm is based on continuous-variable quantum computing architecture resulting in exponential speedup over classical methods. We derive a simple form of the Hamiltonian including interactions and a straightforward implementation of the constraint due to gauge invariance.

Figure 1

One-loop contributions to the scalar mass renormalization.

Figure 2

One-loop contributions to photon field (charge) renormalization.