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.