  Separating the cosmological redshifted 21-cm signal from foregrounds is a
major challenge. We present the cross-correlation of the redshifted 21-cm
emission from neutral hydrogen (HI) in the post-reionization era with the
Ly-alpha forest as a new probe of the large scale matter distribution in the
redshift range z=2 to 3 without the problem of foreground contamination. Though
the 21-cm and the Ly-alpha forest signals originate from different
astrophysical systems, they are both expected to trace the underlying dark
matter distribution on large scales. The multi-frequency angular
cross-correlation power spectrum estimator is found to be unaffected by the
discrete quasar sampling, which only affects the noise in the estimate. We
consider a hypothetical redshifted 21-cm observation in a single field of view
1.3 degrees (FWHM) centered at z=2.2 where the binned 21-cm angular power
spectrum can be measured at an SNR of 3 sigma or better across the range 500 <
l < 4000 . Keeping the parameters of the 21-cm observation fixed, we have
estimated the SNR for the cross-correlation signal varying the quasar angular
number density n of the Ly-alpha forest survey. Assuming that the spectra have
SNR ~5 in pixels of length 44 km/s, we find that a 5 sigma detection of the
cross-correlation signal is possible at 600 < l < 2000 with n=4 deg^{-2}. This
value of n is well within the reach of upcoming Ly-alpha forest surveys. The
cross-correlation signal will be a new, independent probe of the astrophysics
of the diffuse IGM, the growth of structure and the expansion history of the
Universe.
