  A quantum algorithm to simulate the real time dynamics of two-flavor massive
Gross-Neveu model is presented in Schrodinger picture. We implement the
simulation on a classic computer by applying the matrix product state
representation. The real time evolutions of up to four particles on a site in
initial state are figured out in space-time coordinate. The state evolutions
are effectively affected by fermion mass and coupling constant of the model.
Especially when the mass of fermion is small enough and the coupling is strong
enough, the fundamental fermions evolve synchronistically in space from the
two-fermion and four-fermion initial states. These are also the conditions on
which the bound states made up of fundamental fermion pairs were found to arise
automatically in the literatures.
