  Continuous-time quantum walks provide an alternative method for quantum
search problems. Most of the earlier studies confirmed that quadratic speedup
exists in some synthetic Hamiltonians, but whether there is quadratic speedup
in real physical systems is elusive. Here, we investigate three physical
systems with long-range atom-atom interaction which are possible good
candidates for realizing the quantum search, including one-dimensional atom
arrays either trapped in an optical lattice or coupled to waveguide near band
edge or dispersively coupled to a good cavity. We find that all three systems
can provide near-optimal quantum search if there is no dissipation. However, if
the dissipation is considered only the latter two systems (i.e., waveguide-QED
and cavity-QED systems) can still have high success probabilities because the
latter two systems can significantly enhance the atom-atom interaction even if
they are far apart and the spectra gap can be much larger which can reduce the
search time and the effects of dissipation significantly. Our studies here can
provide helpful instructions for realizing quantum search in real physical
systems in the noisy intermediate-scale quantum era.
