  In this paper, we considered the study of Friedmann-Robertson-Walker (FRW)
model in the framework of $f(Q,T)$ gravity, an extension of symmetric
teleparallel gravity, recently defined by Y. Xu et al. \cite{Xu}. The
non-linear model $f(Q,T)=-\alpha Q-\beta T^2$, where $\alpha>0$ and $\beta>0$
are constants, is taken into account. The equation of state of perfect fluid is
assumed and 31 points of Hubble data are used to constrain the value of model
parameter. To explore the evolution of the universe, the numerical solutions of
cosmological implications such as Hubble parameter, deceleration parameter,
apparent magnitude and luminosity distance are determined and the energy
conditions are examined. The theoretical results of Hubble parameter are
compared with $\Lambda$CDM model. Further, 57 Supernova data (42 from Supernova
cosmology project and 15 from Cal\'{a}n/ Tolono supernova survey) are also used
to have consistent results of apparent magnitude and luminosity distance.
