Digital Quantum Simulation for Energy Spectroscopy of Schwinger Model

We discuss a method to efficiently compute energy spectra in quantum field theories by digital quantum simulation. We utilize a quantum algorithm called coherent imaging spectroscopy which quenches the ground state with a perturbation oscillating periodically in time for various frequencies and then reads off excited energy levels from values of frequencies having loss of the vacuum-to-vacuum probability by the quench. We demonstrate this method in the Schwinger model which is the (1+1)-dimensional quantum electrodynamics with a topological term. In particular, the ground state of the Schwinger model on lattice is prepared by adiabatic state preparation and then we apply various types of quenches to the approximate ground state via Suzuki-Trotter time evolution. We benchmark the types of quenches and argue their (dis)advantages especially in the context of studying quantum field theories. We also estimate the computational complexity to obtain physically reasonable results which likely implies efficiency of the method in the early fault-tolerant quantum computer era