  This note discusses a method for computing the energy spectra of quantum
field theory utilizing digital quantum simulation. A quantum algorithm, called
coherent imaging spectroscopy, quenches the vacuum with a time-oscillating
perturbation and then reads off the excited energy levels from the loss in the
vacuum-to-vacuum probability following the quench. As a practical
demonstration, we apply this algorithm to the (1+1)-dimensional quantum
electrodynamics with a topological term known as the Schwinger model, where the
conventional Monte Carlo approach is practically inaccessible. In particular,
on a classical simulator, we prepare the vacuum of the Schwinger model on a
lattice by adiabatic state preparation and then apply various types of quenches
to the approximate vacuum through Suzuki-Trotter time evolution. We discuss the
dependence of the simulation results on the specific types of quenches and
introduce various consistency checks, including the exact diagonalization and
the continuum limit extrapolation. The estimation of the computational
complexity required to obtain physically reasonable results implies that the
method is likely efficient in the coming era of early fault-tolerant quantum
computers.
