The jet transport coefficient $\hat{q}$ is the leading transport coefficient that controls the modification of hard jets produced in heavy­-ion collisions. This coefficient is inherently non­-perturbative, and hence, is challenging to compute from first principles. In this report, we present a perturbative quantum chromodynamics (pQCD) and lattice gauge theory based formulation to study $\hat{q}$. We formulate $\hat{q}$ within a 4-dimensional (4D) quenched SU(3) lattice. We consider a leading order diagram for a hard parton passing through the quark-gluon plasma. The non­-perturbative part is expressed in terms of a non­local (two­-point) Field­-Strength-­Field­-Strength (FF) operator product which can be Taylor expanded after analytic continuation to the Euclidean region. Such an expansion allows us to write $\hat{q}$ in terms of the expectation of local operators. Finally, we present our results for $\hat{q}$ in a pure gluon plasma.