  We explore the use of twisted boundary conditions in extracting the nucleon
mass and the binding energy of two-baryon systems, such as the deuteron, from
Lattice QCD calculations. Averaging the results of calculations performed with
periodic and anti-periodic boundary conditions imposed upon the light-quark
fields, or other pair-wise averages, improves the volume dependence of the
deuteron binding energy from ~exp(-kappa*L)/L to ~exp(-sqrt(2)kappa*L)/L.
However, a twist angle of pi/2 in each of the spatial directions improves the
volume dependence from ~exp(-kappa*L)/L to ~exp(-2kappa*L)/L. Twist averaging
the binding energy with a random sampling of twist angles improves the volume
dependence from ~exp^(-kappa*L)/L to ~exp(-2kappa*L)/L, but with a standard
deviation of ~exp(-kappa*L)/L, introducing a signal-to-noise issue in modest
lattice volumes. Using the experimentally determined phase shifts and mixing
angles, we determine the expected energies of the deuteron states over a range
of cubic lattice volumes for a selection of twisted boundary conditions.
