  The proton decay has not been experimentally observed with the lower limit of
the proton lifetime being $\gtrsim 10^{34}$ years which is more than the age of
the universe. One of the important quantity that appears in the study of the
proton decay is the proton decay matrix element which is a non-perturbative
quantity in QCD which cannot be calculated by using the perturbative QCD (pQCD)
method but it can be calculated by using the lattice QCD method. In this paper
we formulate the lattice QCD method to study the proton decay matrix element.
We derive the non-perturbative formula of the proton decay matrix element from
the first principle in QCD which can be calculated by using the lattice QCD
method.
