  We propose a method to map the conventional optical interferometry setup into
quantum circuits. The unknown phase shift inside a Mach-Zehnder interferometer
in the presence of photon loss is estimated by simulating the quantum circuits.
For this aim, we use the Bayesian approach in which the likelihood functions
are needed, and they are obtained by simulating the appropriate quantum
circuits. The precision of four different definite photon-number states of
light, which all possess six photons, is compared. In addition, the fisher
information for the four definite photon-number states in the setup is also
estimated to check the optimality of the chosen measurement scheme.
