  Quantum computers, using efficient Hamiltonian evolution routines, have the
potential to simulate Green's functions of classically-intractable quantum
systems. However, the decoherence errors of near-term quantum processors
prohibit large evolution times, posing limits to the spectrum resolution. In
this work, we show that Atomic Norm Minimization, a well-known super-resolution
technique, can significantly reduce the minimum circuit depth for accurate
spectrum reconstruction. We demonstrate this technique by recovering the
spectral function of an impurity model from measurements of its Green's
function on an IBM quantum computer. The reconstruction error with the Atomic
Norm Minimization is one order of magnitude smaller than with more standard
signal processing methods. Super-resolution methods can facilitate the
simulation of large and previously unexplored quantum systems, and may
constitute a useful non-variational tool to establish a quantum advantage in a
nearer future.
