  We continue our study of the correspondence between BPS structures and
topological recursion in the uncoupled case, this time from the viewpoint of
quantum curves. For spectral curves of hypergeometric type, we show the
Borel-resummed Voros symbols of the corresponding quantum curves solve
Bridgeland's "BPS Riemann-Hilbert problem". In particular, they satisfy the
required jump property in agreement with the generalized definition of BPS
indices $\Omega$ in our previous work. Furthermore, we observe the Voros
coefficients define a closed one-form on the parameter space, and show that
(log of) Bridgeland's $\tau$-function encoding the solution is none other than
the corresponding potential, up to a constant. When the quantization parameter
is set to a special value, this agrees with the Borel sum of the topological
recursion partition function $Z_{\rm TR}$, up to a simple factor.
