Finite Density Algorithm in Lattice QCD -- a Canonical Ensemble Approach

I will review the finite density algorithm for lattice QCD based on finite chemical potential and summarize the associated difficulties. I will propose a canonical ensemble approach which projects out the finite baryon number sector from the fermion determinant. For this algorithm to work, it requires an efficient method for calculating the fermion determinant and a Monte Carlo algorithm which accommodates unbiased estimate of the probability. I shall report on the progress made along this direction with the Pad\'{e} - Z$_2$ estimator of the determinant and its implementation in the newly developed Noisy Monte Carlo algorithm.