  The cross-correlation between the 21 cm field and the galaxy distribution is
a potential probe of the Epoch of Reionization (EoR). The 21 cm signal traces
neutral gas in the intergalactic medium and, on large spatial scales, this
should be anti-correlated with the high-redshift galaxy distribution which
partly sources and tracks the ionized gas. In the near future, interferometers
such as the Hydrogen Epoch of Reionization Array (HERA) are projected to
provide extremely sensitive measurements of the 21 cm power spectrum. At the
same time, the Nancy Grace Roman Space Telescope (Roman) will produce the most
extensive catalog to date of bright galaxies from the EoR. Using semi-numeric
simulations of reionization, we explore the prospects for measuring the
cross-power spectrum between the 21 cm and galaxy fields during the EoR. We
forecast a 14$\sigma$ detection between HERA and Roman, assuming an overlapping
survey area of 500 deg$^2$, redshift uncertainties of $\sigma_z = 0.01$ (as
expected for the high-latitude spectroscopic survey of Ly$\alpha$-emitting
galaxies), and an effective Ly$\alpha$ emitter duty cycle of $f_\mathrm{LAE} =
0.1$. Thus the HERA-Roman cross-power spectrum may be used to help verify 21 cm
detections from HERA. We find that the shot-noise in the galaxy distribution is
a limiting factor for detection, and so supplemental observations using Roman
should prioritize deeper observations, rather than covering a wider field of
view.
