  Three billion years after the big bang (at redshift z=2), half of the most
massive galaxies were already old, quiescent systems with little to no residual
star formation and extremely compact with stellar mass densities at least an
order of magnitude larger than in low redshift ellipticals, their descendants.
Little is known about how they formed, but their evolved, dense stellar
populations suggest formation within intense, compact starbursts 1-2 Gyr
earlier (at 3<z<6). Simulations show that gas-rich major mergers can give rise
to such starbursts which produce dense remnants. Sub-millimeter selected
galaxies (SMGs) are prime examples of intense, gas-rich, starbursts. With a
new, representative spectroscopic sample of compact quiescent galaxies at z=2
and a statistically well-understood sample of SMGs, we show that z=3-6 SMGs are
consistent with being the progenitors of z=2 quiescent galaxies, matching their
formation redshifts and their distributions of sizes, stellar masses and
internal velocities. Assuming an evolutionary connection, their space densities
also match if the mean duty cycle of SMG starbursts is 42 (+40/-29) Myr
(consistent with independent estimates), which indicates that the bulk of stars
in these massive galaxies were formed in a major, early surge of
star-formation. These results suggests a coherent picture of the formation
history of the most massive galaxies in the universe, from their initial burst
of violent star-formation through their appearance as high stellar-density
galaxy cores and to their ultimate fate as giant ellipticals.
