  Correlations and measures of entanglement in ground state wavefunctions of
relativistic quantum field theories are spatially localized over length scales
set by the mass of the lightest particle. We utilize this localization to
design digital quantum circuits for preparing the ground states of lattice
scalar quantum field theories. Controlled rotations that are exponentially
localized in their position-space extent are found to provide exponentially
convergent wavefunction fidelity. These angles scale with the correlation
between sites and the classical two-point correlation function, as opposed to
the more localized mutual information or the hyper-localized negativity. We
anticipate that further investigations will uncover quantum circuit designs
with controlled rotations dictated by the measures of entanglement. This work
is expected to impact quantum simulations of systems of importance to nuclear
physics, high-energy physics, and basic energy sciences research.
