  We show that the reduced $\mathrm{SL}_2(\mathbb{C})$-twisted Burau
representation can be obtained from the quantum group
$\mathcal{U}_q(\mathfrak{sl}_2)$ for $q = i$ a fourth root of unity and that
representations of $\mathcal{U}_q(\mathfrak{sl}_2)$ satisfy a type of
Schur-Weyl duality with the Burau representation. As a consequence, the
$\operatorname{SL}_2(\mathbb{C})$-twisted Reidemeister torsion of links can be
obtained as a quantum invariant. Our construction is closely related to the
quantum holonomy invariant of Blanchet, Geer, Patureau-Mirand, and Reshetikhin,
and we interpret their invariant as a twisted Conway potential.
