  In the present analysis, we explore a new version of dark energy called
Barrow holographic dark energy within the framework modified gravity called
$f(Q,T)$ gravity by adopting the simple homogeneous, isotropic, and spatially
flat Friedmann-Robertson-Walker (FRW) model of the universe. Our goal is to
understand how the universe evolved over time. To do this, we use
parameterizetion of Hubble's parameter method. We then use a powerful tool
called Monte Carlo Markov Chain to find the best values for the constants in
our formula. We do this by comparing our formula to actual data from
observations of the universe. Once we have the best values for the constants,
we calculate other important parameters that describe the universe's evolution.
These include: Deceleration parameter which measures how quickly the expansion
is slowing down. We found $q_0 = -0.601^{+0.0131}_{-0.0131}$. Equation of state
parameter to measures the properties of dark energy. We find $\omega_0 =
-0.7018^{+0.0101}_{-0.0101}$. We also study the stability and energy conditions
along with the state-finder and $O_m(z)$-parameter of our model to ensure it's
consistent with our understanding of the universe.
