  Weak gravitational lensing is becoming a mature technique for constraining
cosmological parameters, and future surveys will be able to constrain the dark
energy equation of state $w$. When analyzing galaxy surveys, redshift
information has proven to be a valuable addition to angular shear correlations.
We forecast parameter constraints on the triplet $(\Omega_m,w,\sigma_8)$ for an
LSST-like photometric galaxy survey, using tomography of the shear-shear power
spectrum, convergence peak counts and higher convergence moments. We find that
redshift tomography with the power spectrum reduces the area of the $1\sigma$
confidence interval in $(\Omega_m,w)$ space by a factor of 8 with respect to
the case of the single highest redshift bin. We also find that adding
non-Gaussian information from the peak counts and higher-order moments of the
convergence field and its spatial derivatives further reduces the constrained
area in $(\Omega_m,w)$ by a factor of 3 and 4, respectively. When we add cosmic
microwave background parameter priors from Planck to our analysis, tomography
improves power spectrum constraints by a factor of 3. Adding moments yields an
improvement by an additional factor of 2, and adding both moments and peaks
improves by almost a factor of 3, over power spectrum tomography alone. We
evaluate the effect of uncorrected systematic photometric redshift errors on
the parameter constraints. We find that different statistics lead to different
bias directions in parameter space, suggesting the possibility of eliminating
this bias via self-calibration.
