  In this paper, we investigate $f(Q)$ gravity ($Q$ represents the
non-metricity) to explore its cosmological implications of the two
non-interacting dark energy models. We use the correspondence scenario to find
the pilgrim and generalized ghost pilgrim dark energy $f(Q)$ gravity models for
a Friedmann-Robertson-Walker universe with pressureless matter and a power-law
scale factor. The reconstructed models explain the observed rapid expansion of
the universe using astronomical observations. We also examine the physical
properties of the model, including its equation of state parameter,
$(\omega_{D}-\omega^{\prime}_{D})$ and $(r-s)$-planes and the squared speed of
sound. It is found that our results are consistent with the interacting pilgrim
dark energy model in the same gravity.
