Abstract:

In a seminal paper on quantum computation of scattering amplitudes, Jordan, Lee and Preskill  motivate their work by stating that perturbative series for real-time evolution do not converge. However, when digitizations and truncations are introduced, this statement needs to be revisited. We show that finite harmonic digitizations lead to weak and strong coupling expansions with finite radius of convergence for lambda phi four theories (systems of coupled anharmonic oscillators). We discuss empirically the complex singularities of the perturbative series in the complex lambda plane and their Riemann sheets. We show that results from algebraic geometry provide a more systematic understanding of these observations. The work was done in collaboration with Robert Maxton. I discuss recent progress regarding the convergence of Dyson’s series, supersymmetric extensions and bootstrap approaches.