  We consider the problem of coded distributed computing using polar codes. The
average execution time of a coded computing system is related to the error
probability for transmission over the binary erasure channel in recent work by
Soleymani, Jamali and Mahdavifar, where the performance of binary linear codes
is investigated. In this paper, we focus on polar codes and unveil a connection
between the average execution time and the scaling exponent $\mu$ of the family
of codes. The scaling exponent has emerged as a central object in the
finite-length characterization of polar codes, and it captures the speed of
convergence to capacity. In particular, we show that (i) the gap between the
normalized average execution time of polar codes and that of optimal MDS codes
is $O(n^{-1/\mu})$, and (ii) this upper bound can be improved to roughly
$O(n^{-1/2})$ by considering polar codes with large kernels. We conjecture that
these bounds could be improved to $O(n^{-2/\mu})$ and $O(n^{-1})$,
respectively, and provide a heuristic argument as well as numerical evidence
supporting this view.
