  In the next decade, the LSST will become a major facility for the
astronomical community. However accurately determining the redshifts of the
observed galaxies without using spectroscopy is a major challenge.
Reconstruction of the redshifts with high resolution and well-understood
uncertainties is mandatory for many science goals, including the study of
baryonic acoustic oscillations. We investigate different approaches to
establish the accuracy that can be reached by the LSST six-band photometry. We
construct a realistic mock galaxy catalog, based on the GOODS survey luminosity
function, by simulating the expected apparent magnitude distribution for the
LSST. To reconstruct the photometric redshifts (photo-z's), we consider a
template-fitting method and a neural network method. The photo-z reconstruction
from both of these techniques is tested on real CFHTLS data and also on
simulated catalogs. We describe a new method to improve photo-z reconstruction
that efficiently removes catastrophic outliers via a likelihood ratio
statistical test. This test uses the posterior probability functions of the fit
parameters and the colors. We show that the photometric redshift accuracy will
meet the stringent LSST requirements up to redshift $\sim2.5$ after a selection
that is based on the likelihood ratio test or on the apparent magnitude for
galaxies with $S/N>5$ in at least 5 bands. The former selection has the
advantage of retaining roughly 35% more galaxies for a similar photo-z
performance compared to the latter. Photo-z reconstruction using a neural
network algorithm is also described. In addition, we utilize the CFHTLS
spectro-photometric catalog to outline the possibility of combining the neural
network and template-fitting methods. We conclude that the photo-z's will be
accurately estimated with the LSST if a Bayesian prior probability and a
calibration sample are used.
