Optimized quantum algorithms for simulating the Schwinger effect
The Schwinger model, which describes lattice quantum electrodynamics in $1+1$ space-time dimensions, provides a valuable framework to investigate fundamental aspects of quantum field theory, and a stepping stone towards non-Abelian gauge theories. Specifically, it enables the study of physically relevant dynamical processes, such as the nonperturbative particle-antiparticle pair production, known as the Schwinger effect. In this work, we analyze the quantum computational resource requirements associated with simulating the Schwinger effect under two distinct scenarios: (1) a quench process, where the initial state is a simple product state of a non-interacting theory and then interactions are turned on at time $t=0$, and (2) a splitting (or scattering) process where two Gaussian states, peaked at given initial momenta, are shot away from (or towards) each other. We explore different physical regimes in which the Schwinger effect is expected to be observable. These regimes are characterized by initial momenta and coupling strengths, as well as simulation parameters such as lattice size and electric-field cutoffs. Leveraging known rigorous bounds for electric-field cutoffs, we find that a reliable simulation of the Schwinger effect is provably possible at high cutoff scales. Furthermore, we provide optimized circuit implementations of both the second-order Trotter formula and an interaction-picture algorithm based on the Dyson series to implement the time evolution. Our detailed resource estimates show the regimes in which the interaction-picture approach outperforms the Trotter approach, and vice versa. The improved theoretical error bounds, optimized quantum circuit designs, and explicitly compiled subroutines developed in this study are broadly applicable to simulations of other lattice models in high-energy physics and beyond.