  In the present article, we construct a 2D formulation of quantum gravity in
the framework of a deterministic theory. In this context, a Quantum stationary
Hamilton-Jacobi equation is derived from the Klein- Gordon equation written in
the presence of a gravitational field. We show that this equation reduces to
the Quantum stationary Hamilton- Jacobi equation when the gravitational field
is not present in the 2D time-space. As a second step, we introduce the quantum
gravitational Lagrangian for the quantum motion of a particle moving in the
presence of a gravitational field. We, deduce the relationship between the
gravitational quantum conjugate momentum and the velocity of the particle.
