  We demonstrate how to make rigorous predictions for electroweak matrix
elements in nuclear systems directly from QCD. More precisely, we show how to
determine the short-distance contributions to low-momentum transfer electroweak
matrix elements in the two-nucleon sector from lattice QCD. In potential model
descriptions of multi-nucleon systems, this is equivalent to uniquely
determining the meson-exchange currents, while in the context of nuclear
effective field theory, this translates into determining the coefficients of
local, gauge-invariant, multi-nucleon-electroweak current operators. The
energies of the lowest-lying states of two nucleons on a finite volume lattice
with periodic boundary conditions in the presence of a background magnetic
field are sufficient to determine the local four-nucleon operators that
contribute to the deuteron magnetic moment and to the threshold cross-section
of n + p -> d + gamma. Similarly, the energy-levels of two nucleons immersed in
a background isovector axial weak field can be used to determine the
coefficient of the leading local four-nucleon operator contributing to the
neutral- and charged-current break-up of the deuteron. This is required for the
extraction of solar neutrino fluxes at SNO and future neutrino experiments.
