  Topological quantum field theories with gauge group $\textrm{SU}_2$ associate
to each surface with marked points $\Sigma$ and each integer $r>0$ a vector
space $V_r (\Sigma)$ and to each simple closed curve $\gamma$ in $\Sigma$ an
Hermitian operator $T_r^{\gamma}$ acting on that space. We show that the matrix
elements of the operators $T_r^{\gamma}$ have an asymptotic expansion in orders
of $\frac{1}{r}$, and give a formula to compute the first two terms in terms of
trace functions, generalizing results of March\'e and Paul.
