  We consider a quantum gravity register that is a particular quantum memory
register which grows with time, and whose qubits are pixels of area of quantum
de Sitter horizons. At each time step, the vacuum state of this quantum
register grows because of the uncertainty in quantum information induced by the
vacuum quantum fluctuations. The resulting virtual states, (responsible for the
speed up of growth, i.e., inflation), are operated on by quantum logic gates
and transformed into qubits. The model of quantum growing network (QGN)
described here is exactly solvable, and (apart from its cosmological
implications), can be regarded as the first attempt toward a future model for
the quantum World-Wide Web. We also show that the bound on the speed of
computation, the bound on clock precision, and the holographic bound, are
saturated by the QGN.
