  We give a dimension independent formulation of the quantum search algorithm
introduced in [L. K. Grover, Phys. Rev. Lett. {\bf 79}, 325 (1997)]. This
algorithm provides a quadratic gain when compared to its classical counterpart
by manipulating quantum two--level systems, qubits. We show that this gain,
already known to be optimal, is preserved, irrespectively of the dimension of
the system used to encode quantum information. This is shown by adapting the
protocol to Hilbert spaces of any dimension using the same sequence of
operations/logical gates as its original qubit formulation. Our results are
detailed and illustrated for a system described by continuous variables, where
qubits can be encoded in infinitely many distinct states using the modular
variable formalism.
