  The primordial matter power spectrum quantifies fluctuations in the
distribution of dark matter immediately following inflation. Over cosmic time,
over-dense regions of the primordial density field grow and collapse into dark
matter halos, whose abundance and density profiles retain memory of the initial
conditions. By analyzing the image magnifications in eleven strongly-lensed and
quadruply-imaged quasars, we infer the abundance and concentrations of low-mass
halos, and cast the measurement in terms of the amplitude of the primordial
matter power spectrum. We anchor the power spectrum on large scales, isolating
the effect of small-scale deviations from the $\Lambda$CDM prediction. Assuming
an analytic model for the power spectrum and accounting for several sources of
potential systematic uncertainty, including three different models for the halo
mass function, we obtain correlated inferences of $\log_{10}\left(P /
P_{\Lambda \rm{CDM}}\right)$, the power spectrum amplitude relative to the
predictions of the concordance cosmological model, of $0.0_{-0.4}^{+0.5}$,
$0.1_{-0.6}^{+0.7}$, and $0.2_{-0.9}^{+1.0}$ at k = 10, 25 and 50
$\rm{Mpc^{-1}}$ at $68 \%$ confidence, consistent with cold dark matter and
single-field slow-roll inflation.
