  Laboratory experiments have the capacity to detect the QCD axion in the next
decade, and precisely measure its mass, if it composes the majority of the dark
matter. In type IIB string theory on Calabi-Yau threefolds in the geometric
regime, the QCD axion mass, $m_a$, is strongly correlated with the topological
Hodge number $h^{1,1}$. We compute $m_a$ in a scan of $185{,}965$
compactifications of type IIB string theory on toric hypersurface Calabi-Yau
threefolds. We compute the range of $h^{1,1}$ probed by different experiments
under the condition that the QCD axion can provide the observed dark matter
density with minimal fine-tuning. Taking the experiments DMRadio, ADMX, MADMAX,
and BREAD as indicative on different mass ranges, the $h^{1,1}$ distributions
peak near $h^{1,1}=24.9, \ 65.4, \ 196.8,$ and $310.9,$ respectively. We
furthermore conclude that, without severe fine tuning, detection of the QCD
axion as dark matter \emph{at any mass} disfavours 80% of models with $h^{1,1}
=491$, which is thought to have the most known Calabi-Yau threefolds.
Measurement of the solar axion mass with IAXO is the dominant probe of all
models with $h^{1,1}\gtrsim 250$. This study demonstrates the immense
importance of axion detection in experimentally constraining the string
landscape.
