  We construct a tessellation of AdS$_3$, by extending the equilateral
triangulation of AdS$_2$ on the Poincar\'{e} disk based on the $(2,3,7)$
triangle group, suitable for studying strongly coupled phenomena and the
AdS/CFT correspondence. A Hamiltonian form conducive to the study of dynamics
and quantum computation is presented. We show agreement between lattice
calculations and analytic results for the free scalar theory and find evidence
of a second order critical transition for $\phi^4$ theory using Monte Carlo
simulations. Applications of this AdS Hamiltonian formulation to real time
evolution and quantum computing are discussed.
