Context : In the next decade , the Large Synoptic Survey Telescope ( 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 .

Aims : Reconstruction of the redshifts with high resolution and well-understood uncertainties is mandatory for many science goals , including the study of baryonic acoustic oscillations ( BAO ) .
We investigate different approaches to establish the accuracy that can be reached by the LSST six-band photometry .

Methods : We construct a realistic mock galaxy catalog , based on the Great Observatories Origins Deep Survey ( GOODS ) 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 Canada-France-Hawaii Telescope Legacy Survey ( CFHTLS ) data and also on simulated catalogs .
We describe a new method to improve photometric redshift 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 .

Results : We show that the photometric redshift accuracy will meet the stringent LSST requirements up to redshift \sim 2.5 after a selection that is based on the likelihood ratio test or on the apparent magnitude for galaxies with signal-to-noise ratio 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 .

Conclusions : We demonstrate that the photometric redshifts will be accurately estimated with the LSST if a Bayesian prior probability and a calibration sample are used .