Quantum information theory is undergoing rapid development and recently there has been much progress in
mapping out its relationship to low dimensional gravity, primarily through Chern-Simons topological quantum
field theory and conformal field theory, with the prime application being topological quantum computation.
Less attention has been paid to the relationship of quantum information theory to the long established and well
tested theory of gravitational dynamics of 3+1 dimensional spacetime. Here we discuss this question in the
weak field approximation of the 4-space metric tensor. The proposed approach considers a quantum algorithmic
scheme suitable for simulating physical curved space dynamics that is traditionally described by the well known
Einstein-Hilbert action. The quantum algorithmic approach builds upon Einstein's veirbein representation of
gravity, which Einstein originally developed back in 1928 in his search for a unified field theory and, moreover,
which is presently widely accepted as the preferred theoretical approach for representing dynamical relativistic
Dirac fields in curved space. Although the proposed quantum algorithmic scheme is regular-lattice based it
nevertheless recovers both the Einstein equation of motion as an effective field theory and invariance of the
gravitational gauge field (i.e., the spin connection) with respect to Lorentz transformations as the local symmetry
group in the low energy limit.